Does tube testers tell how much life is left for tubes?

Let's say that you have new tubes, very old tubes that are almost to die, and something in the middle.
What kinds of reading do you expect from these three kinds?
Can you usually tell the life of tubes from tube testers?
How about the color? Do those three kinds of tubes have different colors when they were turned on?
I would like to know when to change tubes before it gets too late.
Some says if it sounds good, don't bother to change. 
Some brands of power/pre amps consume more on tubes than other brands and their life seems varies brand by brand. 
You can take a brand new tube that tests perfectly (this is after all the way they leave the factory) put it in your amp and watch it blow the first week.

You can take another brand new tube that tests perfectly put it in the same amp and it lasts five years.

So yes you can use a tube tester to tell you how long a tube will last. Accurate to within 5 years.
The best measure of the condition of the tube is to measure transconductance.  Transconductance is a measure of the change in current flow across the tube ("plate current") for a given change in grid bias.  (I didn't look that up, so if I got it wrong, mea culpa.) Since it is a current divided by a voltage, its units are inverse to ohms, called "micromhos".  So far as I know, the only vintage tube testers that measure transconductance are Hickok brand and a few other brands that were actually made by Hickok for that brand.  So, you start with a table of transconductance readings for the particular tube under test, and you use the tester to find out whether that tube sample meets spec.  Typical Hickok testers have a big analog meter on the front panel and will indicate to the user whether the tube needs replacement if it is too far under the standard transconductance for that tube type.  Many times a perfectly good usable tube will measure a little below max transconductance.  When the tube is really at death's door, it will look to be very low in transconductance.  Another way to test a tube is simply to measure current and voltage while it is in the circuit where you are using it.  That's actually better than using some ancient uncalibrated tester.  The old testers almost never can test a tube under the actual conditions of its use in circuit, because they usually cannot develop adequate plate voltage or current for high current tubes to work best.
A calibrated TV-7 was good at that, checking life and shorted tubes, i have used one for some time, could not match tubes though. If going into tube testers and want matched tubes better invest on a modern one that can measure in actual conditions, or close, transconductance, plate current, leakage and mu.
Otherwise use your tubes close to the safe end of their lives.
Tubes are not created equally so you cannot tell from heater element glow if they are good or bad.
Actually you cannot tell if they even work.
You could monitor though a specific tube for changes in glow with usage.
Thanks for the info (even to MC).
I have two tube testers. One from Knight and one from Superior Instrument. Both is I guess made in late 50s or early 60s. They don’t have transconductance readings. They tell whether tubes are good or bad, but they don’t tell how much life is left.
If in doubt, I would just purchase new tubes to be safe.
The new (old) preamp I just bought (A.I. M3B) is recommended to have tubes replaced every two years. Yikes!

short answer is even the best tube testers measure the present degree of mutual transconductance of a test subject tube - it is a decent proxy for tube strength/freshness but it is a poor proxy for durability as a function of time

if you want to educate yourself more... - see section on tube testing
An approximation of tube life can be found from the cathode emissions, which I think some testers can provide.

When the cathode electron emission drops way low the tube is at the end of its life.

Tubes can test good right up to the end time of failure.
RIght, the testers can tell you whether or not the tube is OK. They can not tell you how much time is left on the tube until the tube starts to measure poorly which means the tube is at deaths door. I use tubes until they fail and in my experience they sound just fine until they do fail. 
I always keep a full set in reserve. If one tube fails I replace the whole lot unless that particular tube was obviously defective. I keep my phono stage on in standby. The tubes, 6922's last an average of 6 years.
different tubes age in different ways

6dj8 6922 types, in my experience, get noisy with tube ’rush’ or hiss, and microphonic long before they quit entirely - not sure why this happens in the physics occurring inside the tube as time passes -- these will test fine on the tester for gm but then plug em into the linestage or phono stage and they are unlistenable

depending on the application, that change defines their effective ’use-ability’

other tubes may age differently... typical power tubes usually get dull in sound (lose treble detail imaging etc etc) as they get into last 30-40% of their lives

In the end, we usually are alerted to the possibility that a tube or tubes are failing by the fact that the our system sounds "off", not as good as usual.  Only then are we motivated to test tubes.  At that point, if any tubes measure low in transconductance, I ditch them in favor of new.  That nearly always results in restoration of SQ.  I own an ancient Hickok 533A, which I can use to test small signal dual triodes only, to include octal based tubes like the 6SN7 and 6SL7, and it is not much good for testing modern very high transconductance triodes like the 5687 group or the 6DJ8 group, because of its current limitations.  I just shoot for an approximation of "good" with those.  The 533A is no good at all for testing the monster 7241 triodes in my power amplifiers, and for that I just go by listening and then measuring the tubes in situ.  The 7241 is a US milspec power triode developed for use in radar installations.  It can easily run on up to 1A plate current, although I do not stress them that much.
I've just came up with an idea how to deal with when to change tubes. Always have spare tube sets ready. Then, if suspicious, change the tubes. If it sounds much better after the change, keep the change. If the difference is subtle, put the old tubes back and keep listening until feeling suspicious again.
6dj8 6922 types, in my experience, get noisy with tube ’rush’ or hiss, and microphonic long before they quit entirely - not sure why this happens in the physics occurring inside the tube as time passes -- these will test fine on the tester for gm but then plug em into the linestage or phono stage and they are unlistenable
The Following is a recent report I received on a Early 60's produced Valve.
It covers the Anode and Mutual Conductance.
As can be seen each Valve has a very good reading compafrd to a New Factory Spec Valve , whicch is the 100% readings.
What is not shown is if here is a Cathode  / Heater Leakage that if present can impact on a Valves Function for the worse.
  Tested on my uTracer @ 90V -1V

100% is 15mA Ia , 12.5mA/V gm
Valve 1

Section 1 – 17.16mA / 12.37mA/V
Section 2 – 16.13mA / 12.39mA/V

Valve 2

Section 1 – 17.39mA / 11.84mA/V
Section 2 – 18.92mA / 13.16mA/V