When I talk to Gwen, one of the people in Garl's room (in the bandit camp just south of Shady Sands), I get an option the says "I'm [player name], what do you do around here?". When I click on it, it just exits the conversation.

I dunno, it's not exactly serious, I'm just trying to make conversation on a dead board.

Beside officials, there are unofficial patches for both FO1 and FO2, I dont think any of them are included in GOG version, though some resolution patches and such are.

Not sure if this specific one is amongst the fixes, but I'd guess there's a fair chance.

http://fallout.wikia.com/wiki/Fallout_patches

The savegame will almost certainly fail if you patch the game halfway through.

Well, the latest patch approach for Fallout 1 (integrating everything from the Wikia page) is Fallout Fixt by Sduibek
http://www.nma-fallout.com/showthread.php?194562-Fallout-Fixt-alpha-6-7-2-January-29-2014