Not so sure about that because Anti-Monitor eventially consumes the Anti-Matter universe as well in COIE, iirc, so he ate/absorbed his own powersource that he was already connected to gain what? I think it's just that he and Monitor are opposites and equals until AM's actions tipped the balance. There's obviously a connection betwen them and the matter/anti-matter makeup of the DC Multiverse, but I don't believe they both have the equivalent power of half a multiverse each. The Anti-Matter Universe (there was only one) was equal in size to the positive matter multiverse (positive matter being split up into various universes). Once AM started consuming those universes the power balance shifted from equal to anti.
It also made no sense that Monitor didn't just engage him in combat before he began the universe absorptions, but you know.
*edit
Just to clarify, I think there's a connection, but not necessary that the entirety of multiversal halves were all "power source" for the Monitors, just had an effect on their reserves based on the balance.