Yes, miner subscribes to extranonce changes and receives extranonce updates just like job updates. If miner does not subscribe to extranonce, server will never send mining.set_extranonce. With set_extranonce, next work has to be built with new extranonce. The sequence of methods send from NiceHash is following when switching order:

mining.set_extranonce
mining.set_difficulty
mining.notify

That means switching order is as fast as changing work/job. No more reconnects. If there are orders paying less than what you want, you will be of course disconnected.