No, not possible. As in: the remote site does not forward DHCP requests to he local site. This is becasue those are broadcast addresses which are NOT transmitted outside the Ethernet segment - i.e. they do not cross over the router.
Yes, it is possible. You need to set up a DHCP relay system on the other side (can be part of the router) to forward DHCP requests to the Windows server. Then you set up a normal segment in the DHCP server.
That said, the idea may be terrible. Problem is - whenever the link is down, and a computer gets online during this time, it ets no ip address and pretty muc hthe user needs to restart (unless you want to talk users through command line "ipconfig /renew"). DHCP has no concept (unlike IPv6 in general) for assigning addresses to computers post network activatio. Technically you would be better off to get a small servre and put it at the remote site. This can be a small ATOM based thing. This can serve as:
* Local DHCP Server
* Local Domain controller (same problem - link down, things get bad).
* Local DNS server.
* Possibly local file store, at leat for a special admin share so you have afast access to your tools.
If you dont trust the remote site, using 2008 R2 yo ucan make the controller a RODC (Read Only Domain Controller). It sitll will stabilize operations.
I would consider it bad practices to supply DHCP from your central site.