Unless synergy has explicit support for WoL (it didn't last time I used it, but it's been years), it won't just work.
You'd need to patch the synergy server to send a WoL magic packet[1] to wake up the client whenever it sends a message that might hit a client that's asleep. (some systems might support something other than the standard magic packet, but I don't know of anything else that works consistently cross platform.) Might also need to look at making sure the client connection comes back up clean and have some delay to make sure it's ready to receive whatever message started the process, and doesn't timeout while waking up.