What correlation does ping latency have with high server activity?

Typically ICMP ping packets are processed on the NIC and don't tend to go through the upper levels of the OSI model for processing. So typically this is not the case. However it's possible that the NIC activity would impact its ability to respond to packets. If the NIC(s) are exceptionally busy they could create queuing and processing delay on the NIC which might result in higher ping response times. A much better way to understand what's going on with the servers is to monitor them using a passive response time monitoring solution. These types of solutions provide a way to passively understand what the real application traffic is like for the servers of interest, including traffic volumes/rates, response times from the server, session and load indicators. If you also monitor these servers with SNMP you would get greater visibility into discards, buffer queue depth, and error rates on the interfaces at the time utilization is high. These metrics tend to provide you greater visibility to understand what's going on at the time of peak activity levels for optimizing performance.