Do Alerts (Email based on last_receive or last_send) Impact Server Performance?

If your server was running at normal sustained usage of 60% then no.  The alerts you described would not noticeably, negatively impact server performance.  Since you mentioned your server is currently strained, adding an alert might contribute to a negative impact.  In a tipping point sort of way. It would not, however, be the long pole in the tent.  Other processes contributing to the strain would be more culpable.

I have found that things get weird when the server is at a 90-100% capacity.  Things that weren’t a problem are suddenly a huge problem when the server gets squeezed.

One approach we have taken is to replicate our production interfaces in a testing environment and perform simulated load testing.  Pushing our Prod clone to its hardware limits. That has allowed us to identify the bottlenecks in a controlled and measured fashion.  Allowing us to take the “benchmark before you optimize” approach to development. It has also allowed us to test the effectiveness of alerts. Helping us answer questions like:  “Would a last_recieved threshold that is appropriate for Monday 10 am be appropriate for Sunday at 3am?”