GPS, yes. Navigate, not unless they used an app like
MyDirections and set it to navigate. Maps navigates by latitude/longitude. When you give it an address, it uses a Google API to look up the lat/lon of that address, so it needs a data connection, mobile or WiFi.
MyDirections stores locations by lat/lon, so it gives Maps a lat/lon to go to, so Maps doesn't need a data connection for that (and it gets its current location, second by second, from the GPS receiver, which doesn't use data). But they'll have to download the map of the areas they're going to be in while they're still connected to WiFi, or they'll be given navigation instructions on a grey screen. (It's trivial - I have the maps for my entire city [granted, it's not the Greater Los Angeles Area], so I can navigate without data if I want. [I usually don't - I can't get Bluetooth and radio from the head unit at the same time, so I have my favorite radio station streaming on the phone - by data - while I'm navigating. But that's by my choice, not by need.])
No need to close the Google account - you can use the same account on the S5. Just remove the account from the S4.