Yeah, it's OK to squeegee RC prints. Just make sure your squeegee blade is clean and in good condition, as well as the sheet of plexi. The emulsion is the side where you need to take care.
I angle the print slightly on the plexiglass so that one corner of the paper is about 1/8" off the edge. I grab this corner when taking the paper off to flip over to the other side, which keeps you from damaging the paper with a fingernail. I use a piece of plexi larger that the paper itself. Doesn't matter if the plexi is wet or dry, but I do squeegee off excess water between prints. You can do front or back first, I've never seen any difference. Modern RC paper is very durable.