
Sometimes...
I have in excess of 15,000 connections on our mail server, various stages of connections.
See little *IF ANY* performance degradation. The only time I see degradation is when multiple connections are pulling lots and lots of data at the same time...
Idle/persistent connections... pretty much take very little memory and processing to handle.
We are talking a very very significant number to hurt any modern machines. (Modern being anything newer than 4-5 years old)