Double check your scope on the DHCP server, It almost sounds like DHCP is not seeing a valid scope definition for this subnet. Make sure your router address is correct in the scope options.
Try removing the scope and re-adding it from scratch to see if you may have something entered incorrectly that you're not seeing.
Woah, there. What you're saying contradicts itself. You say "single subnet" in one point, but then "VLAN each site" in the second point. Then you say "the networks will NOT be routed". Are you sure you know what you're saying here?
Typically 802.1q VLANs are deployed in a one-to-one relationship with IP subnets. Each 802.1q VLAN acts as an independent Ethernet broadcast domain and, as such, broadcasts from one VLAN (like, say, a machine ARP'ing for another machine in the local subnet) won't be forwarded between the VLANs. Splitting a single IP subnet across multiple VLANs requires a "smart" bridge that can do proxy ARP.
How are you planning to get ARP to work between these various VLANs?
If you really want to eliminate "cross-site 'chatter'" then what you really want is a subnet for each physical location, a router at each location connected to the "MAN" to route traffic to the other locations, and "ip-helper" functionality in each router to forward DHCP requests from the various locations to the central DHCP server.
What it sounds like you don't want is a single big subnet with a bunch of bridges running proxy ARP, in my opinion. Your DHCP inquiry really, really speaks to an underlying desire (though you don't know it) to have per-location subnets with DHCP scopes for each.
To speak to your question specifically re: DHCP: A DHCP "scope" is a range of IP addresses and options that a DHCP server will "hand out". The DHCP server chooses the scope to choose an address based on either the network interface the request is received from (if it's a broadcast request) or the address of the DHCP relay agent (if it's a relayed request).
Some background: Best way to segment traffic, VLAN or subnet?
Best Answer
Yes it is a bad idea.
The Cisco documentation says this, "The helper address can be a specific DHCP server address, or it can be the network address if other DHCP servers are on the destination network segment. Using the network address enables other servers to respond to DHCP requests."
While this will save you work short term, the end result is that any rogue DHCP servers (accidental or malicious) in that /16 will be able to hand addresses to your entire network as well. This doesn't seem like a good trade off to me.
If you are looking to save work, why not re-use the existing DHCP server IPs on the new servers?