You need to tell us more about how your network is set up.
If you're on a DHCP network, then no, it's unlikely since the DHCP server will automatically resupply your MAC address with the same IP it's had. You can try and request a new DHCP ID via the Network prefpane, but most likely you'll end up with the same IP address. Unless you can ask the network admin, there's no way to know (AFAIK) what the time out on the supplied address is. 1 day, 3 days, 10 days, forever? Who knows?
If it's a static IP.. you should know about those already, no?