This can be done, but I don't know if it will provide any benefit to you:
User comes online from AP1, DHCP discover is received by the modem and relayed to the DHCP server, response is sent back and the user receives and binds to IP.
User crosses the threshold and changes to AP2. Because the media has changed, the user will re-discover and perform the DHCP process again. They will most likely be allocated the same address again (presuming the lease hasn't expired or been administratively removed), but you're still re-binding the IP. Because you are re-binding the IP on the User, any open TCP connections would likely be severed.
I think that this is what you're trying to avoid by allocating the same address across all devices, but please do correct me if I'm wrong.