Firefox is the only browser I'm really familiar with. As far as I know, any official build that has ever been released has shipped with pipelining turned off (ie. sending multiple requests instead of sending them sequentially). Chrome and FF do use prefetching though (loading content in the background that has not been explicitly requested by the user), but even that should only result in no more than one simultaneous connection.
I suppose Google Analytics or some other tracking service might provide some more insight into how many users are browsing the site at any given time. Some people, like me, prefer not to be tracked and attempt to block any such tracking scripts, pixels and cookies but I doubt it's a statistically significant number of people.
I got the redirect last night. I posted on your blog when it happened. It said something about 300 connections at the bottom then, I was able to access the site about an hour later.
Interesting also; I've always had a BLF button on the top menu bar of my browser and after getting that redirect last night, the logo changed to a little blue drop looking thing with eyes at the bottom - Drupal logo?
I got error 403 forbidden to access webpage or internet explorer could not connect to the web address. It attempts to connect to BLF for about 30 secs before I get one of those errors. Never got the 300 connections thing. Happens to me at around 11:30 am to about 3:30 pm UTC+9:30