Question for amp experts

Is it technically possible for Active speakers to sound as good as great separate amps? 
Technically? No. 

Take your imaginary great sounding amp. Now imagine that amp inside a speaker. No way it will sound as good as outside away from all that speaker vibration. The speaker also will sound better with its crossover further from the power supply, etc, of the amp. 
Yes, it possible for them to sound even better.  The key word is synergy.  The amp can actually be matched to the driver.  Additionally, the crossover is easier to implement.  This applies to both analog and digital designs.  Although it is most common, the amp and crossover do not have to be placed within the loudspeaker cabinet.
theoretically speaking if same amp used yes, but with a seperate one no. And still you will need a preamp. Vibration issues and interference with crossover can be minimized to a point with construction. I cannot imagine a tube amp inside a speaker cabinet.

Good points. I know many of the wireless desktop, active speakers have preamp, dacs, built in. Be a pain if you wanted to add a TT. 
I believe it may be, for the reasons given by @onhwy61 
If not, then explain the success of ATC speakers.  I came very close to going in that direction after a frustrating 5+ years of looking for an amplifier that would sound great in my system.  I probably would have ended up with ATC SCM 100s if not for my new SMc amplifiers.
I'm no expert but most all subwoofers are active speakers. A lot of studio speakers are active. Maybe it has more to do with the target market. 
My Studio Yamaha active monitor sounds great with recordings. If Yamaha made tower versions, I'd be interested for a second system
Bang & Olufsen Beolab 50 and 90?
Sure and add the Dutch&Dutch 8c and the Kii Three speakers, as well as some pro models.

There's no reason active speakers (with DSP) cannot equal and exceed the performance of passive loudspeakers.  It is only the influence of marketing and engrained bias that stands in the way.
Not for the same price (price of amp included in speakers vs. separate amp).  Amp designers have to envisage a wide range of loads, though not everything from very high to very low sensitivity.  Amp inside speaker--the designer knows exactly what all the measurements are, so in theory the match can be as perfect as possible ($$ permitting).  Add in digital correction, and we're going to see more products like the Dutch & Dutch.  Buchardt already announced...
There are a lot of variables. Theoretically 'yes', in practice yes if the separates aren't that good to start with (IMO).
Yes especially if I get my hands on them!

Happy Listening.
Yes, as Millercarbon say, there are some space and cooling limitations to an active speaker, but with money, many can be overcome. So in theory, not impossible at all. And as also noted, there are significant opportunities when one can fully characterize both the load and the transfer function of the speaker - and in effect compensate for those irregularities.  In a cheap, mass-fi world this is precisely what Bose does and what every expensive in-car manufacturer does. Why? because cars are insanely irregular acoustic environments and benefit dis proportionally.  While i have not heard the latest, i think the flagship Meridian system is a case for the active approach.
Now most active speakers are far more compromised, but we must still compare an active speaker at $2k, with, say a passive speaker at $1k and a relatively modest -- and imperfect -- power amp at another $1k. Better? dunno - let your ears judge.  A simpler package? You bet. And for some that will win right there.
Control theory is a powerful concept. It is the basis of most rocket science and robotics and self-compensating weapons. Active speakers are how one implements control theory in the music world.
Whether the practitioners get it right is another question.

That depends on the money , and compared to what 
If is hooked up internally just using a module and internal digital board no.
Many commercial loudspeakers speakers are active designs.  Think concerts, studio monitors, etc.  

I think digital actives like those from Meridian are really impressive and worth a listen.  You have to remember that you are getting a dedicated amplifier for each speaker driver.  Everything is matched by design.  The older Meridian speakers like DSP5000s, 5500s and 6000s all use class A amplifiers, and are available on the used market at a fraction of their original prices.  It can be a lot of trial and error (and $) to match speakers, amps, components and cables in a conventional system.

To address an earlier point, the components need not be in the speaker cabinet for an active speaker design- NHT had an active model where the electronics were in a module separate from the speaker cabinet.
Anybody who thinks a class d amp sounds good has never heard a good amp. Anyone who thinks an amps chassis makes no difference has never heard a great amp.
" While i have not heard the latest, i think the flagship Meridian system is a case for the active approach."

Not even close.