Yes, it's possible. You'll need gpspipe, which I have built. (And it may be available elsewhere, too.)

You'll need to establish a link between the two, presumably with rfcomm, but then it'll be reasonably straightforward:
Although I'm not sure the device name is rfcomm, I have vague memories; substitute whatever the real value is.

But it's not necessarily easy; might be better off getting a better BT GPS.