With SNMP monitoring is this okay to run on a Server? Would that actually be the best place for it to run?
All depends on how busy your server currently is, what it's specs are, etc. Can't really give you an answer other than "try it out and see" without knowing your situation.
The snmp processes can sometimes use a lot of resources.
I've never had a resource issue for monitoring SNMP but Dan is right, it is subjective to specifications.
What ever you do, in the monitor set (especially if you are worried about resources) don't collect data for the set at -1 (Always) We did this for hundreds of devices and nearly crashed our VSA, it was logging 260,000 alerts a day. I know it is off topic, but plan what you want to collect, where and when. If you have the model of the server i might have a set for it already and some rules set up around it.