Yes, your position is shown on the map. Forgot to mention an offline mapping app for Colorado named Cotrex.

You can test out how they work in just a few minutes by making a pdf map of your home location (I only use caltopo right not), uploading to your phone (or just using the caltopo app). It might can all be done on the phone although Caltopo has been taking features away from the phone that may be on their desktop website, because they have paid subscriptions for more full-featured use.