It should have basically no impact.
I just logged in to our New Relic to see if I could get you a report, but Fatal Error Notify doesn’t even show up in the breakdown of resource use by plugin.
When PHP shuts down (https://www.php.net/manual/en/function.register-shutdown-function.php), FEN checks to see if there was any error during the page load. If there was, it sends you an email.
In the Pro version you have the ability to send multiple alerts to different destinations: email, Slack, and SMS.
If you configured all three alert types, this could take a second or two to send the data, but that would only be in cases where an error was detected that needs to send a notification.
The plugin doesn’t monitor the site logs, it just checks for a fatal error each time the page load is finished ✅