GPS is a pretty passive system
[pedantic ON]
Not that passive.
AFAIK all modern radio receivers are superheterodyne receivers, which means they have a built-in oscillator which resonates at the reception frequency.
So they do radiate some (small) amount of energy.
[pedantic OFF]
I do agree however that it is much less than a cell phone trying to connect to the network (especially when it "sees" a dozen cells)
[Edited for spelling]