I'm confident that nagios can do this yes. Nagios is meant to be used to monitor anything that can be reached via ip.
You really need to read the docs. Setup nagios, get it running, take a look at what you now see, and make any changes you need to. Perhaps creating hostgroups as the docs suggest will organize the hosts into groups. I find that the names given to hosts makes all the difference in the world too. That way, as an admin, all the hosts are grouped together alphabetically.