Q: Should there be any play on the CV shaft where it goes into the transmission?

Typically, on the inboard joint of a CV axle, you will be able to readily detect (feel) movement because the shaft into the transmission rides on a bushing that has some clearance. If the movement is "excessive", that could mean the bushing is worn. On CV axles, if there is noise it is usually from the outboard joint, simply because the extent of movement there, and the angles and mechanical loads, are much greater than that placed on the inboard joint. In your circumstance, if you suspect the noise is coming from the inboard area, or the transmission/differential itself, it might be necessary to apply remote "chassis ears" (wireless microphones) to identify the actual origin of the noise. Also, of course, bad wheel bearings, can cause noise, too, that might sound like the transmission is "failing". If you desire that a certified mechanic evaluate this, simply request a noise diagnostic and the mechanic will pinpoint the source and then estimate the repair cost for you.