Will Solar Cells charge under a clear plastic sheet?
It will definitely work, but it's interesting to talk about some consideration.

Depending of the technology of your panel, the spectral response may vary. It is likely that you are using a c-Si panel (this is the most common where you can see cells).

c-Si panel will convert most of the energy on the infra-red band of the spectrum from about 400 to 1'100nm that you mostly cannot see with your eyes. 

A plastic that is transparent for you may not be transparent on this spectral band but you can very simply test that by putting the sheet in front of your panel and measuring any drop in the short circuit current (you won't see any significant difference in the open voltage).

Another point raised in the comments is the UV instability of polymer and you may want to have a plastic which is UV rated so it won't break appart after a few months.