“Can I put myself at a place on the map where I am certain of the exact spot, and then use that information to navigate via the onboard maps and compass?”
Yes. You could measure the length of the GPS, say four inches. Then with a compass you could determine magnetic north. So, if you wanted to travel one mile south from your current destination, by placing the GPS on the ground and moving it south, one length at a time, you could use the GPS to travel 3 X 5280 GPS unit lengths in the south direction.
You could even measure the height of buildings with your four inch GPS unit. You could measure the length of the GPS’s shadow and then measure the height of a building’s shadow and by similar triangles, you could calculate the building’s height.
Wait, there’s more. Using a teeter toter, you could calculate the weight of objects using your GPS (assuming you know the GPS’s weight). Balance an object on the teeter toter against the GPS and it’s weight is inversely proportional to the ratio of the distances of the GPS and the measured object from the fulcrum.
So, no, your GPS is not a paper weight.