If the computer is operating with no permanant external antenna etc. (i.e. no permanant installation), wouldn't it be similar to an unapproved GPS, and not need approval? Or does the fact that it's using signals not usually used by aircraft make it different?
A lot of modern laptops have 3G modems built-in (particularly business-oriented builds, a lá Lenovo et al), so you wouldn't even need a dongle, just a sim (which you could probably borrow from your phone, in a pinch).