As far as I know, they are not related. If I turn off push, either on my jailbroken iphone or my girl's unjailbroken one, GPS and maps keep on working just fine.
edit: Reading little bit more on pushfix I'll try to explain what became clear to me.
Push and Maps or GPS are still unrelated.
Jailbreaking is a legal procedure to make your iPhone free from "apple locks". That's where the name came from.
With that, a jailbroken iPhone can do things apple doesn't allow, but without a proper tool installed "jailbreaking" does nothing.
pushfix is a tool to fix a problem on the push notifications brought by activating the iphone without an authorized SIM (a.k.a. Hacktivated iPhone). pushfix was further improved to fix other problems, probably brought by the same Hacktivation, such as Wifi and GPS.
I highly recommend you do a lot more research and get familiarized with the terms and issues related to iPhone (yes, that's a lot of reading and quite complicated) or just get an Android! ;)
Here are some good starting points (other than the link already provided):
And some good sources: