Is there any downtime during plan migration? E.g. when upgrading or downgrading plan?

It depends. If you have a 2+ nodes cluster, there will be no downtime during the migration.

If you have a 1-node server, then there will be downtime. How long time it will take depends on the length of the queues you have (usually a short downtime). Please note that messages, exchanges, and queues that are not durable and persistent will be lost during the migration.