GPS does not measure slant distance. It measures as if there is a vertical axis representing the waypoint from ground level to infinite height.

Using GPS for navaid substitutions will be easy if you have a non-GPS approved approach loaded as an advisory-only approach. This is a good practice to increase situational awareness. Load your advisory approach at the same time as setting up for the non-GPS approach, and if it is a second or third approach to the same airport you might do that during the missed approach legs. Any navaid for substitution would probably be already there. If not pull out the righthand knob, turn counterclockwise and you will get a list of the nearest 20 navaids. Do a direct-to the one you need for substitution. This will work best if the GPS is already up and running with at least the current destination in play, again this is a good practice to cultivate.

My instructor used to say use all your equipment. I kept that in mind until I got this one old airplane with a worn out Loran, wing leveler that thought a 5 degree bank was level, and a weak ADF.