I am trying to test a new SNMP server (Nagios Core) along side the current one (Check MK) which has already been running for quite some time now. Will this cause any problems on an agent device (Cisco Catalyst 2960X), if a second SNMP server is added on with the first one?
Short answer: It may.
Network devices usually don't have powerful CPUs and I've seen devices running into timeouts when more then one system was polling data via SNMP. It all depends on how much data you poll, how often you do this and if the device CPU is currently busy with something else. I'll guess the only thing for you to do is try it and keep a close eye on your systems while doing it.