With iOS, no. With Android, yes.
Apple has gone to great lengths to limit what apps can do. You can do some things in the background for an extended period of time (GPS, play audio, Voip, etc), but after a reboot your app will not be restarted until the user opens it again. There are exceptions to this. Voip apps are allowed to restart after a reboot, but apple will not approve your app for the App Store unless you actually have a place for a user in your app to use the Voip feature. Geofences are a possibility, but I haven't had experience with that feature yet. In my experience, Apple does whatever they can to make sure your app doesn't run forever.
With android, there is more flexibility and what you propose is totally possible. I've listed some important links below, since most of those solutions are far better documented than what I can do here.
Essentially you need to register as a boot receiver and then send an intent to start a titanium android service when the boot event is received. I don't have experience with starting a titanium service, but I'm sure its a simple intent you need to fire. Either way you'll need a module for this native code. I attached a link to a bencoding titanium module that may help you, although there may be some others out there. You may even need to code one yourself.
Samsung is notorious for stopping your app with their SPCM feature. You may want to familiarize yourself with it. I've added a stackoverflow discussion link below.
I don't know all of your system requirements but honestly, for any app I would try my best to not run forever. It will hurt the battery life for your users and will add a lot of complexity. Maybe you could simply have the app check the GPS coordinates when it receives a push notification and decide right there and then whether to present a notification to the user? Just something to consider.
Either way good luck!