While I’m not sure if Twitch limits the number of IRC accounts that can connect from a single IP I do not see any policy reasons why you couldn’t use different accounts.
My concern would be scalability since you would need to maintain an active connection for each user account that is active regardless of how many message it is actually sending in chat. You would also need to strictly enforce the 20 in 30 rate limit for each account to avoid an IP block since you can’t be sure each account is modded in chat or whitelisted as a bot (and you shouldn’t expect Twitch to respond to whitelisting requests for a hosted service like this which also means you can’t use whispers).
I probably would stick to each client maintaining the IRC connection on the remote machine but still route the business logic through the server so messages must originate there before being sent to the client to send to chat. So if the client is reverse engineered it could still connection to chat but wouldn’t be able to reproduce your service.