Do they need to unmount my unit when being serviced? 

Actually, it is a case to case basis, and sometimes if the AC unit has not been serviced for a long time, then there are big chances that it needs an overall dismantling. Regularly, here are the following expectations that you should set: 

Overhaul servicing – requires an entire dismantling of the unit

Chemical and Normal servicing – requires a partial dismantling of the unit parts