Na, your clients will not find out new SEPM automatically,
Clients communicate with SEPM using Sylink.xml file, this file has SEPM IP address and communication port, smc.exe will read this file ( based on heartbeat) to check for any new policy or updates.
if your SEPM is replaced or does not exist, clients will still try to connect your old sepm as it has the sepm details in the sylink file, The easiest way is to use the communication deployment wizard to push out new sylink so that clients get hooked to the new sepm.
if you are in 11.x u need to use the sylink replacer utility