Good morning,
The first P2 Vision series came out in 2013 and I've never heard of anybody successfully upgrading the GPS, although it's been discussed before. So I would say no.
If you look at this video and shoot ahead to 5:30
you can see he also has dashes, so I don't think that is your problem.
Are you sure your GPS doesn't work? If the GPS or compass doesn't work, the lamps in the rear will indicate an error and the motors won't start. They are very reliable. I've flown over a thousand miles with them and haven't had a single problem. The modules, used, are cheap these days - around $20. If you have a cracked antenna and you're interested in replacing it, it's even cheaper.
Otherwise any problem can be solved with some copper shielding.
Test it with open sky above and around you. No buildings or trees blocking. Check satellites availability for a given time and day here:
www.uavforecast.com
It is possible to connect the compass to the GPS module if you wanted. The older style has a compass in it and also a plug for the compass connection. On the newer style the plug is missing, but it might still have the compass in it, I'm not sure. You might do this if you had some kind of whacky modified legs and no place to put the compass on the leg.
You can also get one of these:
Amazon.com: DJI NAZA-M V2 GPS Module: Electronics
But you should be sure it includes a mount which would put it on a plastic stick up and above the AC. This would bring the GPS module far enough away from the wifi module so as to eliminate any interference. It includes a compass - the compass data is sent to the FC via the same GPS cable and plug. You'd have to drill holes into the AC for both the mount and the cable.
Good luck