Does after insert trigger cause delay?
The question is not the same, but my answer is:  https://dba.stackexchange.com/a/159012/1876

Don't use Triggers; instead batch the data and batch the processing.  It is a lot more efficient than doing everything one row at a time, especially when a spike occurs.

Another issue... If you let "too many" connections get started, yes, the entire system can stall.  This is sometimes because MySQL (and the OS) are carefully parceling out resources (CPU, I/O, etc) to more clients than the resources (cores, etc) can handle.  Throughput may be fine, but latency suffers terribly.