Technically to pinpoint your location via GPS, no.
However in order to speed up the GPS lock, you really need cellular data. It's hard to get a GPS only lock in a city with high rises. You need to stand on the roof, and even then it can take 30 seconds.
As for mapping, you need to make sure if you have offline maps. If you do have offline maps it may be theoretically possible to do fully offline navigation with GPS only. The issue is that the GPS antenna in general on phones isn't as strong as a standalone unit, say like a Garmin. As a result your lock times will be pretty horrendous on GPS only. IF you're in the suburbs it may work well, and I think the only challenges you may have could be on cloudy days. If you do intend on doing GPS only, I would recommend an app like GPS Status where you can download GPS location info for a week ahead. Use it to update GPS location info everytime you're on WiFi, so it can help boost your lock times. I found that it's a good help up to 2 days ahead, but the older the location data is, the slower your locks become.