Sometimes, depending on the network card and the OS software. For example, in FreeBSD you might use:
ifconfig de0 ether 01:23:45:67:89:ab
I understand Linux has a similar ability, and I think Windows XP can do it in a much more GUI-ish way. Some routers have a "clone MAC address" ability. This won't change the MAC address kept in the ROM, so the command has to be re-done every time the machine boots.
When using DHCP or BOOTP, the IP address may be assigned based on the MAC address due to the configuration of the DHCP server (or it might just take an available currently-unused one from the pool). Note that an unrecognized MAC address might be denied service entirely rather than given a different IP. This depends entirely on how your ISP set up the DHCP server.
If a machine is manually assigned an IP address or it is being assigned an IP address from a DHCP server that YOU control, you may assign any IP address. There's no magic formula that you can use to calculate an IP address from a MAC address.
Gordon L. Burditt