Is the side to side movement in the universal shafts something that should be tested for play? How much movement is acceptable or is this even an item for concern?

Do you mean CV constant velocity joints?
Side to side in relation to the car? yes the shaft can move a fair bit in/out.

If you don't know the history, it has ripped boots, leaking seals, leaking grease, etc it's time to service them.

Sometimes the clip will come loose and allow more side play. You will hear it rub.
The axle really won't go anywhere though.