What MarXtar said.
As an exercise in "COULD it be done" - you could PROBABLY hack away at the WDS PXE server, and inject our boot images, but that'd be needlessly painful & high in maintenance. Easier to use what's been created for it - the Client Self-Electing Platform (CSEP).
That means you CAN leave it running on a single server (essentially - reusing your existing WDS server) or be more network friendly & have CSEP set one up at each site / broadcast domain and have the network stuff no longer forward UDP / PXE requests across the corporate network (which usually network people would be quite grateful for in my experience).
While the Core *CAN* have the PXE rep stuff installed on itself, it's discouraged to do so in live environments (it's usually fine for testing). As was pointed out, it's not a supported config -- and while for testing it's usually fine, there's usually too much chance for things to go awry (usually "at the worst time possible") and if it ends up taking bits of the Core Server with it (and/or IIS) then that'll really get you in trouble.
If you're absolutely in a dearth for a box (it does NOT have to be a server - we're quite shameless & able to use regular clients as PXE reps) then you can use your Core - but you will want to move away from that as soon as possible.
Does that (along with MarXtar's explanation) cover about everything ?