Silly Question...does a transport have a "sound" ?

I'm thinking of upgrading to a dedicated transport (like an Accustic Arts Drive I, AM Mephesto II.X or even a ML 37) from the Sony DVP-9000es I'm using now. I'm locked in on my dac (Kora Heremes II), which I love.

My question is, do transports from different manufacturers have significantly audible "sonic signitures" that I should consider when deciding what to mate to the Kora? (e.g., hifi-ish/fast/cold/analytic vs. analog-like/polite/bloomy/warm).

To go even further down this slippery slope, are there discerable differences between, say, a Teac VRDS 3.2 mechanism and a Phillips CDM Pro2 or a C.E.C. belt drive?

I've read a lot of posts here and on AA that've provided some clues, but was wondering if anyone with significant experience with multiple brands of transports could share some of their experiences.

In other words, is the transport "sound/signiture" something worth paying a lot of attention too, or should I just worry about mechanical things like stability, isolation, etc. Thanks.