One of the reasons I never completed this game on the C64 back in the day is because of being very limited in when and where I could save the game. Does the gog version running in DOSBOX support saving the game at any time or does the save system work the same as in the original game?

The original save system is in place for this version. The only places you can save are at the Inn and in camp. There is a different version of DOSBox at http://ykhwong.x-y.net/ which does allow save states. You'd have to run and configure the other version of DOSBox manually.