I want GPS in my watch, like the S2, but don't want to pay a monthly carrier fee. If I don't activate the carrier fee (AT&T, T-Mobile, Verizon, etc.) ,will the watch's internal GPS still operate?
The S2 has no GPS receiver in it (see https://www.gsmarena.com/samsung_gear_s2-7678.php ), so you'd have to connect it to a phone - but the phone's GPS will operate without being activated. (The map app won't show a map without a data connection, though, unless you've downloaded maps to the phone.)
The 3G Gear S2 does have GPS, but the question is will it work stand-alone without having a data plan. I would guess not in stand alone, but it would using the GPS/data from your phone.