League-of-legends – Do towers and/or minions regenerate health

Sadly, there's no sure-fire way of resolving this situation.

You won't be able to rely on minions to take out their towers and nexus, especially if their uber status gets to the point where they can start defending their respawning inhibitors. If you get really lucky and get their nexus towers down, you could just farm minions hard enough for yours to take the nexus down a bit then try to dive the nexus. I'd consider this a Hail Mary more than anything else, though.

If you know you're going up against a team that is going to steamroll you once they get maxxed out (2+ carries), the main goal is to take advantage of the fact that they will be weaker in the early game. If you zone the carries and/or kill them enough to keep them from getting geared and leveled, your team will get powerful enough to take their nexus before they can do anything about it.

Assuming you find yourself in that unfortunate position anyway and forcing their team to split up isn't working, you absolutely have to focus the primary damage dealers down first. If they stick together and you're not killing their carries first, you'll take way more damage than you will deal out over the course of the fight and you're sure to lose.

Considering the item options you can get at the start of the game, health pots really aren't a bad choice. Depending on what kind of lane you're going to play, champions often choose if they want boots or a bigger item first. If you go boots, you have that extra gold to spend. Why not spend it in a constructive and inexpensive way such as health pots?

Health pots are particularly effective for junglers. It gives that extra health boost they need in order to clear more camps before going back and buying.

The benefit is definitely worth the cost.