Does a cheap cd transport create poor digital copies?

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...