"At the beginning of any round, if you successfully released a Channel ability in the previous round, you can spend 1 MP to immediately Channel".
Yes, if in Round 1 you released a channel ability, then at the start of round 2, you can spend 1 MP and start channeling. This don't count as a turn, doesn't take an action, so you're free to do whatever you want during your 2nd turn.
Skalds are very good at chaining together channel effects each round, as long as they have the MP to continue.