I would suggest you send a polite email or letter to the head of sim, worst is that they can say no, but either way it shows your interest and he/she may remember your name in the future!
As a former sim instructor I would only allow company personnel to observe, again with the sole permission of the students. I would suggest you observe a training day or recurrent training. As said above, an extra set of eyes during a check is generally not appreciated by most crews.
In my opinion, it would be beneficial to you, you can see what to work towards, learn something, and ask questions! The deal clencher for me in becoming a pilot was sitting on the jump seat as a teenager, alas not allowed anymore! As I said, first port of call should be head of sim/training manager. All the best for the future!