It really shouldn't draw all that much, as it was designed to run off battery power.

What's the specs on the fuse? I'm not sure whether they have it to protect the car or the GPS, if it is 3A it's probably there to protect the car. But you could throw in a really low rated fuse (i.e. 250ma, or 500ma) then it should at least make sure that the GPS doesn't draw too much, and going from very low (100ma?) you could iteratively find exactly how much it draws.