Will my car's AM/FM antenna boost the signal of a tablet/carputer GPS?
No, it will not help. GPS uses a much higher frequency than FM radio and trying to receive that with an FM antenna will not work well at all. Also, GPS signals are circularly polarized while FM signals are linearly polarized, so not only will you be operating way outside of the antenna bandwidth you will also have a polarization mismatch. If you want to use an external GPS antenna, I recommend either a patch or a helical antenna with an integrated LNA our complete GPS receiver to avoid cable losses.