Tough question. IMHO antivirus seems to mostly for compliance purposes (filling the checkboxes) and not necessarily as a real asset for security.
Not only will they only detect things they already know about, they often enhance the attack surface and place themeself in a position where they are the best target for an attacker (root permissions or even integration in the kernel).
Does this help you so far? Probably not, but I would advise to put work where it is more useful, e.g. hardening systems (using SSH keys instead of passwords, keeping software up to date, removing old programs if they are not used anymore, allowing user only to access machines where they need to be, using password managers, good firewall rules, etc.) and to try to get a better overview about what is happening in your network.
As for the concern about the antivirus hindering Icinga (and other software):
This is likely, since Icinga executes other programs (check plugins) VERY OFTEN, that an antivirus might singnificantly incress ressource consumption. It seems like you already notice that in the configuration validation stage.