Does a cheap cd transport create poor digital copies?

I want to load some CDs onto the hard drive of a music server via a USB port. I have a quality USB cable, but I’m wondering if using a standard issue external CD drive ($50 type thing) as a transport will imbed the common cheap player problems onto the stored music (jitter, etc.)...or does it simply create a digital copy of the original onto the player?

I’m not going to run out and buy a transport as my CD collection is limited, but I am curious about this and maybe it will help others. Anyone know the technical facts or have an opinion?

The program Exact Audio Copy will make a bit perfect copy of a CD as long as the disc has no serious physical defects.  It does not matter what CD ROM drive or USB cable is used.  There may be other programs that do the same things these days, but EAC was the standard in live music recording/trading circles for many years.
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EAC and DBPoweramp both seconded.

As long as the disc can actually be read, the copy will be perfect. The copy can in fact end up being better than the original, if the latter originates from the end of the run of a stamper.

A pressing plant will often use their stampers for longer runs than are advisable in order to save on cost, with the result that the last CDs in every run end up being difficult or even (very rarely) impossible to read. A successfull copy, on the other hand, will always be perfectly readable.
I’ve used EAC in the past and agree it works well. 

My Sony z1es has cd import software, and has a error check option that takes about 4x longer. So this does answer my question, I’ll just  import directly to the hard drive via USB from the external disc drive, and this should create an exact dupe. 

Thanks for the assist, much appreciated. 
I suspect a CD can be read poorly intruducing errors. See the wikipedia for the Red books spec. There is some error corrction but not very strong. The PCM encoding of the digital output of a SPDIF has an analog component, as you will find out if you plug it into a line input on your preamp. How effective accurate the embedded clock is another discussion. ESS adresses data stream clock recovery in their better chips. SPDIF is compromise for convenience that lacks a distinct clock signal. 
Errors on the disc surface may be enough for a disc read to fail. If a transport is better at handling this it may also be better at handling less intrusive errors. 
The near realtime nature of SPDIF is a clue to how little processing buffering is actually done.
Old technology.

"I suspect a CD can be read poorly intruducing errors"

The point of using a program like EAC or DBPoweramp is that, if you choose, error won’t be accepted. If the disc can be read, a perfect copy will be made. If it can’t be read, a copy will only result if you’ve chosen settings which allow errors, hence allowing one to be made.

My own experience, with a thousand CDs or so, indicate that CDs which cannot be copied perfectly are very few and very far between. Off hand I believe I remember having trouble with 3.
Hey, anyone know why CD copies can sometimes sound better than the original or is that an old wives tale?
That argument goes both ways.  I used to think that CDRs sounded better than the originals, and that CDs from aHD bested the originals, but with the improvement in DAC technology over the past few years I’ve swung the other way.  I’ve seen reports that copied CDs have either more or less jitter, sometimes from the same writer...
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I am referring to plain ordinary CD copies, no fancy editing or upsampling or whatever.
Perhaps CDRs are easier for players to read than commercially produced CDs.  Totally guessing here.
" Hey, anyone know why CD copies can sometimes sound better than the original or is that an old wives tale? "

Yes. See above.