Clash-of-clans – Is it possible to raid or be in the same league as a clanmate in multi-player

tl:dr Yes it is possible, but they have different town hall level requirements and costs, so you have to have a high level village with substantial resources to purchase both.

Barbarian King - Available at Town Hall level 7, and costs 10k Dark Elixir. This means you can potentially purchase him without spending money if you build and completely fill the Dark Elixir Storage which is also first available to you at TH level 7. Note that you can do this by spending gems, or by raiding - but you don't get a Dark Elixir "mine" till TH level 8. (It's painfully slow, so don't hold your breath waiting for it).

Archer Queen - Available at Town Hall level 9, and costs 40k Dark Elixir. This is substantially more than what your early Dark Elixir Storage can hold, so effectively you'll have a hard time getting her early on without spending gems. If you are very patient, or a very successful end game raider, then you may eventually get her without spending money.

SuperCell, the game's creator, has provided this resource for those curious about matchmaking and how trophies work.

To summarize, it is completely dependent on your number of trophies in relation to your opponent's. If your opponent has significantly more trophies than you, you will gain a lot more trophies than usual if you win offensively or defensively. The opposite also applies, where if you lose an attack or defense against someone with less trophies than you, you will lose more trophies.

Level of town hall or any other building has no part in the calculation.