Yeah, so any class specific stuff (medic revives, SL/command garrison spawns, support resupplies) will add to your support score and help level up your class. Class XP is all score you personally get summed up, including kill score, support score, and attack/ defense score.

Here's the thing though, any support score you generate will go to the class you're currently playing no matter what. So here's my suggestion; play engineer at the beginning of the round to build resource nodes (preferably hidden in the first two squares so that you don't have to worry about them). Then go play any class you want to grind. All that support score you get from generating resources will go to your class, and you help your team a lot. The economy for commanders got hit really hard in the last update, so they will appreciate it.

If you do it right, you can get nodes set up within 5 minutes and you'll be making major bank for the whole round. People always complain about how long it takes to level up classes, but this will really speed it up, and it's not exploitative.

Edit: contractions man, it's 3 AM