Can I switch A instead of U in Accessories

The reason for "switching" the U (AC Common) I believe is that you can activate the accessory off a section of isolated outside rail of the layout.   The reason to do this is to activate the gateman or the switch tower operator "when the train arrives"...  

If you're using traditional track you need to either purchase a special track section where one outside rail has cardboard or plastic insulators so that it's "isolated" from the other outside rail.... If you're using Ross, Gargraves, Atlas the two outside rails are already isolated from each other..

The A post is AC Hot, the U post is common...   The AC Hot should be connected to the center rail, and the common U connected to the outside rails..   You are correct that not all Lionel transformers are exactly the same, you need to check the operator's manual to know which posts are hot and which are common.  

Hope this helps. 

My question really is will I damage anything if I hook a wire from the A post of the transformer to the U post of the accessory and from the U post of the transformer  to the A post of the accessory. (The accessory being either the Lionel Gateman or the Lionel switching tower,)

No damage.

The one thing you need to watch is that the base of metal accessories to not tough the metal ties on the track.  Frequently on metal accessories. like the flood light towers, the entire frame is energized with either A or U. These need to be kept away from metal track or other accessories that may be at a different potential.