It really depends on the dhcpd config of the network you’re connecting to.
In our environment, we lock down our dhcp setup so that authorized machines have their MACs mapped to static IPs in various subnets, which are defined per functional group, while unauthorized machines that plug into a physical port are assigned an address out of a general pool that is locked down by our firewall to essentially be Internet only.
If I’m interpreting your question correctly, will your laptop get another address, then answer should be yes, as soon as a physical network connection is sensed, the NIC in your laptop should do a dhcp request broadcast out to the local subnet and wait for a response. From there (assuming the local dhcpd or equivalent is accepting requests) the negotiation for a new lease should commence.
I’ll admit that my dhcp is a little rusty; if you want a definitive and thorough answer, I recommend you slog through RFC1541 (http://www.rfc-editor.org/rfc/rfc1541.txt).