DVR6K - My GPS III Pilot worked brilliantly. I had a window seat, but windows on a CRJ700 aren't too big (in fact, nothing on a CRJ700 is very big), and yet it still worked fine sat on the tray.
rolling circle - Garmin, Bendix/KING etc make aviation GPS units. These GPS units are for use in aeroplanes. That's what they do. I don't think they'll be taken off the market any time soon due to your personal testing requirements. :-)
Irrelevent technical comments aside, I guess the polite thing to do is ask and have it cleared by flight crew.