Shimming Engine for Header Clearance

No that will not work. Even if you succeed, wouldn't that make the drive line end up out of alignment and start vibrations that could cause other problems.

Yes it will mis-align the drive shaft a little. If the front of the engine moves toward the passenger's side then the tail of the trans should pivot over to the driver's side. One solution usually creates two problems!! But if you scoot the trans mount over the same amount (in the same direction) then you should be OK.

treblig