Is it possible to disable all mysql_connect(): Too many connections emails, but not other errors? Right now I get about 4000 emails daily from this error as I run a DB backup that clogs up the DB for a few mins ant these emails are getting enormous.

Wondering if its possible to stop mysql from sending me emails about this
The answer is that, disable your mailer on the script that checking for this error. Look for the script and comment out the mailer.