Help with understanding number of managers

I new to Docker and just trying to get my head around the best way to setup a swarm. I planning on having a 3 node swarm so I have a choice of 1 or 3 managers. From what I read so far I understand the performance would be better with just 1 manager but if the manager was down you wouldn’t be able to do any management tasks until the manager had been recovered.

The part that I not sure on is if the single manager went down leaving the 2 workers would the swarm still be working and would the services running still be accessible.