Though you can open but you'll get watermarks and there will be a hat kind of icon on the files which differentiates student version files from commercial ones.
There should be no problem doing that. A Solidworks file is a Solidworks file.
As long as it is a .sldprt, .sldasm, slddrw it should be fine.
As long as the releases are the same. Meaning you can't open a 2010 file up
in 2009, but you can open a 2009 file up in 2010
I have a more watered down version of Solidworks at home vs work and I am able to
open the same files up in both going back and forth.