Not really, not if we're only talking about using a small fraction of the total power of a ZPM, which IMO is actually highly likely, take a fraction of the 3000 odd years a ZPM powered the city's shields.
It would depend on if you can gather enough energy from the geothermal source(s) quickly enough, but you could still fill a large capacitor to power anything you like.
You haven't in any way proven that, I'm talking about just raising the shield, maybe have it up for a little while, long enough to hold back an attack from the Wraith and maybe mount a defense against them (firing off a few drones or getting a 304 back to Earth).
A total ZPM isn't needed to just raise the shield, or hold back a Wraith attack for a few hours, only a fraction of it's total power is needed for that, depending on how many days the Wraith were attacking and how many ships they were using it could be less than 1% of a ZPMs total energy output.