Your server will get a different IP address. DHCP servers use the mac address of a machine to track assigned Ip addresses.
I don’t recall if there a DHCP DISCOVER or a REQUEST is sent first.
BTW: Just an obversation: Server’s shouls use static IPs, or at least have a DHCP reservation setup. (Of course, the reservation is keyed off the MAC address, so you’ll have to change the reservation when changing the NIC.)