No, mosh doesn't work like that. You can turn off the network connection in one of the nodes (both the server and the client) for hours and when they come back you still have your session like it was before the connection dropped.

I do this everyday on the client side (taking my laptop to work, opening the lid and having my session going on), and sometime on the server side as well.

Only if keepalive is disabled; in which case regular SSH will work the same way.