If I set up a new DHCP server on this
* Will it know the leases? (Maybe the information is stored in AD?)
The lease are stored in %systemroot%\system32\dhcp as dhcp.mdb and temp.mdb. (Reference) They are not stored in AD, and will not be replicated.
* Am I going to have to make everyone reboot so there are no conflicts?
No need. Just configure Windows DHCP to check for an existing client on that IP (right click on the server in the DHCP tool, there is an option to have Windows DHCP check up to 5 IP's before handing one out).
* Anything else I should consider?
Configure a secondary backup DHCP server using the 80/20 rule. Printers should have their IP's statically assigned (now is a great time to check!), as should other essential system hardware (routers, WAP's, etc).