Richard is correct. If you really wanted to get a little "fun" time in the box, you could hang out late at night and get to know the sim tech's at your airline.
I also agree that getting some real sim time to prep for an interview is worth it's weight in gold. Each box has its own feel, some of the old ones don't fly at all, some of the new ones are pretty darn good. Spending some money for the sim prep will pay for itself a thousands times when you get the job!
Generally speaking, the simulators are pretty busy. Our contract requires that we get the daytime use of the box. New hires get checked at O-Dark-Thirty in the morning, and the company rents the box to other users at night - so there isn't much unused time in a day.
As far as check rides. They have "first look" maneuvers that you are being evaluated on such as V1 cuts, Non-precision approach (one or two engine), engine out landing, engine failure during a missed approach, rejected takeoff, and Cat II. They want to see how you do on this stuff coming into the box, pretty much cold. If you were to get some sim time before going to recurrent training, it would defeat the purpose of first look maneuvers and skew the data they collect from it.
Going to recurrent is stressful, but it can be fun once you get in the groove and relax a little. Besides, I've never crashed a simulator so bad that I couldn't walk away from it!