The GPS bands are far from the public service bands. Also GPS/Sat antennae are optimized to receive signals in the vertical plane, that is from the sky. Further it would require adapters and impedance of the cables would likely be different too. I would not expect this solution to work well.
The only other solution that you might consider is a glass-mount antenna. I am not in love with them but are readily available even from Radio Shack, Catalog #: 20-011. I am not in love with it because it is rather long but requires no drilling.
I did not see the specific item you are talking about. Just a couple of things to keep in mind though: If an antenna does not explicitly say that it is for mobile installation, do not assume that it is. Be sure that you are getting an SMA connector, and as I may have mentioned before you will probably want a 90 degree adapter on the radio end. In my experience, a HDTV antenna in connected to a HP-1will improve analog reception in a vehicle or at least not hurt it. That being said, as expected I suppose, it seems that this setup favors UHF AND 800 MHz systems. There is scant use of VHF Low in my area so I can't say for sure but I do not expect one to get much performance in this band.
Yes, unless you are able to choose expedited service it will take weeks to get your item. In any case if you can, let me know how it works out and post some pictures as well!