DHCP under Windows these days is really pretty good about that. I've seen addresses come up nearly instantly the moment the DHCP server was back on-line.
The problem is more on the boot side. It can take many seconds longer to boot as the machine searches in vain for its address.
Of course, I prefer static IP addressing in home networks anyway.
Good points - I note, though, that WIN98 ain't too good at recovery or initialization compared to XP/2K/2K3.
I use statics on stuff behind a router and NAT and disable DHCP, but the single PC behind a DSL/Cable modem still looks for DHCP and, particularly if it's WIN9X, craps out if the modem isn't there.
I don't think it craps out permanently in Win9x. It can just take a really long time. The only time I've seen it regularly fail to boot is if the Novell client is installed.
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