if you have any binding on your coupler, it'll hurt something, either pinion support, tail bushing, or the coupler. It needs to be aligned so it slides easy. You might need to add turnbuckles to the rear of the trans for fine adjustment as it's literally half a turn on a 3/8unf thread from binding up. If you have no trans mount, a 1/4in 6061 motorplate isn't ridged enough to hang the trans from unsupported and it won't slide free unless supported.
I disagree re the mid plate. If the motor is not bolted to the other side maybe the plate could flex enough to cause a problem, especially if the frame is excessively wide or the top and bottom rails don't have much vertical spread and are low relative to the crank centerline. I never run a trans mount in my cars and never have problems with binding. In the case of a car where the trans coupler plugs directly into the female unit on the rear end the alignment is more critical but there should not be any issues if the car is built correctly.
I have seen issues when the mid plate is not supported correctly as in a car where the motor has been moved forward from the original location as in an old car that was not built with enough room for a transmission (right Steve? 
) but in general a transmission mount is not a really good idea or necessary when you have front mounts and a mid plate.
Roo
I always thought the same Roo until this car I have now. It's a shortly glide with a straight male / female coupler (not the nice in situ version). The motor was set using a line up bar and presumed aligned. When we mocked up, whatever we did we couldn't get the coupler to slide easy. We assumed alignment was off, so it was sent away again to have it re-done on the jig, new motor plate and chassis mounts reamed to the bolt shanks (with engine weight on mid plate ears). We aligned the coupler on a scissor jack so it slid easy, then made the front motor plates with saddle mounts, using transfer punches and again reaming all holes to size to take out any slop. This was closer but again it bound up. Talking to another racer with the same set up who had the same issue, we made two turnbuckles mounted off the trans rear cover triangulated down to two brackets on the chassis. We found the range of adjustment to be within half a turn on the bars and just taking up the trans weight slightly was the difference between it binding and sliding freely.
A mount may not be needed for all cars but this was the only way we could obtain the alignment. With a shortly glide close coupled we didn't have the driveshaft length to take up any angular mis-alignment. With a full length glide and a driveshaft, I wouldn't expect to use a mount either. I should add both couplers were brand new and with used / worn couplers I imagine this might not have been so much of an issue.
Heres a pic, you can just see the rod end on the rear cover
