On Apache/PHP, most persistant connections are opened on a per backend basis. i.e. each backend opens its own persistant connection, not to be shared with the other backends.
So, if your apache is limited to 100 children, then you could theoretically wind up with 100 or more persistant connections.
In general, unless you are running a TRULY loaded server (lotsa ram and lotsa users) it doesn't gain much to use persistant connects, but can easily cause problems.