With a DHCP reservation that doesnt matter as the client will always get the same IP, the DHCP server will not assign that IP to any network card other than the one that has the MAC address that the reservation was set up with.
To be honest even without a reservation it is extremely likely that a device will get the same IP when its lease expires because when half of its DHCP lease has expired it will begin to request a renew from the DHCP server (and the default DHCP lease time is 8 days so you have got 4 days for the client to be booted up at least once for that same IP to be leased to the same client). Also I think DHCP servers are encouraged (by the DHCP RFC) to give a client the same IP that it had previously when it requests a renew.

Anyway, geek talk aside, why have the server cluttering up the network with broadcasts every 10 seconds when you could just have the client application broadcast when it starts up and then have the server respond when it receives this broadcast... 1 broadcast each time the client app launches sounds much better than a broadcast every 10 seconds to me