Multiple handlers in same endpoint and worker process

We currently have a worker process, call it worker-A, that handles 3 types of messages (so 3 handlers). This process runs on 8 servers, along with 7 other worker processes. I understand that worker-A uses the same underlying MSMQ queue for all 3 message types. The load for those 3 message types is pretty low. However, these messages need to process relatively quickly, writing to a SQL db, as there is external batch process that reads the records off of SQL db every 5 minutes and processes them.
We are considering running an another message type through this worker (new handler) that will have a much heavier load around 2PM daily of up to 25K messages that will ultimately call Twilio to send SMS message to users. My question is if the current messages, which have a higher priority than the new SMS messages, will get delayed if they come in during the high load times and will be queued behind the bulk messages. Or, if because they are handled by a different handler, will they be unaffected and process in parallel?