Maybe a stupid question...but would it be possible to use a router with some kind of linux firmware and a laptop in a car as a radar detector?
No. For so many reasons. One obvious one:
802.11 = 2.4, 3.6, or 5 GHz
X band = 8-12 GHz
K band = 18-27 GHz
Ka band = 26.5 - 40 GHz
Layman's explanation of the above: The router cannot "tune" to the needed frequencies.
(Then there's the DSSS vs burst detection, etc, etc, etc...)