Escrow contracts in Bitcoin are now more and more used because they add real security without taking much convenience. Shameless plug [0] - I work for a startup that does exactly that, utilizing multi signature Bitcoin addressed for added user security. But you could also build a service for a true escrow very easily and as you say, that wouldn't mean putting all the trust into the escrow party, which is great. These services, in fact, already do exist [1].
Also, at least for P2SH (multi signature/escrow addresses), getting their balance is no different than for normal addresses. Completed transactions to them are perfectly visible on the network so you can sum them up. Uncompleted (partially signed) transactions are not sent to the network though, so you cannot estimate how many "pending" Bitcoins are there for a given address.
What I wonder is what happens to the money locked up in these transactions. I understand that the money is effectively inaccessible to both the sender and the receiver until the transaction is resolved. Is that right ?
I wonder about the implications of that, since it effectively takes money out of circulation, during whatever length of time it takes to finalize the transaction. That presumably includes any conflict resolution process that may exist ?
The money is sitting on special multisignature address before transaction is resolved. It's a 2 out of 3 address, which means that two signatures are required to move the funds further. The good thing about it is that you can totally skip the escrow party here if buyer and seller agree - they both just sign the transaction and send it to the network. Escrow is needed only in case of a conflict - he would have then to investigate and sign a transaction with either buyer to refund the Bitcoins or to seller to forward them to him as contract described (in a case that buyer disappears for some reason).
This setup has one downside though - if one party sides with the escrow, they could agree to sign a transaction to scam the other party. That's why it is not 100% bulletproof and you have to carefully select your escrow partner so that both parties trust him to an extent.
As for your question - it really depends on the way the contract is structured. In theory you could have a 2 of 3 signature address and a timelocked/nLockTimed transaction sending money to an additional arbiter if the time passes without a resolution.
Also, at least for P2SH (multi signature/escrow addresses), getting their balance is no different than for normal addresses. Completed transactions to them are perfectly visible on the network so you can sum them up. Uncompleted (partially signed) transactions are not sent to the network though, so you cannot estimate how many "pending" Bitcoins are there for a given address.
[0] https://bitalo.com
[1] http://cosign.co.in