I've started playing the game (with the Updated Restoration Project installed) using a stealthy and diplomatic kind of character build.

Is it worthwhile to take the Swift Learner perk as soon as it becomes available, if I'm only going to take it once?
I guess I'm afraid that I'll be losing out on a lot of experience points since I'll most likely either totally avoid or run away from many combat situations (as necessary and when possible), and I feel like I should try to make up for it somehow.

There are plenty of opportunities to get experience from completing quests. Later on in the game, once you get much better weapons and Power Armor, you can get experience from killing enemies that you would normally run away from early in the game. Don't bother with the perk as it's a waste.

I agree, there are far better choices.
.

I do have a question regarding that perk, though: Does the bonus apply only to XP gained from combat, or also from quests and other achievements?

It applies to all experience gained.

I don't really see it apllying to quest XP; only XP gained from using skills and from kills.