You should not give up your most powerful capital ship-carriers to solve a small problem like anti-matter usages and recharges on a colony frigate! Most rapid expansions require more than one colony frigate and small fleets to capture asteroids while you concentrate your capital ship(s) on planets. By small fleets i mean 2-4 scouts and 1-2 frigates.
Fast expansion is also determined by how powerful your capital ship is: Mostly you can make pirates chase your capital ship around the gravity well while u macro fighters to kill off the siege frigrates and long range frigates. This is why carriers are the best for a fast expansion.
No way. If you're determined to use a quick expansion strategy, you absolutely NEED to use a colony cap ship if you want to be most efficient. When I'm using that strategy (which I use a lot) I usually get a colony cap, 11ish combat scouts, a colony frigate, and a few more scouts for capturing extractors or luring planetary militia away. On a great map I can have 5 planets colonized by 6 minutes in.
One couldn't come anywhere close to that if one's using a carrier cap. Scouts are essentially fighters that can phase jump - you don't need to rely on strike-craft for taking out siege frigates.
However: this sort of thing is what to do when focusing purely on economy and expansion. If you're in a more cramped game like a standard random 3v3 to 5v5, the cost of building that many scouts (and having a low-firepower cap ship) can cripple you, so the firepower of the carrier cap is often the way to go instead. (Exception: if you're quite skilled like Auqia or Howthe? and are very much expecting to be able to take many planets, or if you're Vasari with the Evacuator, starting with a colony cap can still work quite well.)
