Will there be a way of confirming the # of coins in existence?
No; knowledge of the secret keys used in the setup would allow someone to create coins out of nowhere, and this would not be detectable in any way.
well, we know how many coins are won when a block is signed and we know how many signed blocks are in the ledger, so I suppose it's simple math.
It's not so simple in Zcash. If there is an exploit or trusted initialization is compromised, attacker could create infinite amount of coins using private transactions and we could never know about it.
Zooko hinted that there is a way to audit total number of coin in existence without compromising privacy. But that is just an alarm to know if we're compromised, it does not mean trusted setup become trustless.