From my understanding, when a new block is mined, the coinbase address's balance is incremented by the block reward amount. If this address had a zero balance before the block was mined and the block contains a transaction that spends funds from this address, would the block be considered valid?
No, the reward is credited after all the transactions in the block are processed.
From the Yellow Paper section 11. Block Finalization
The process of finalising a block involves four stages:
- Validate (or, if mining, determine) ommers;
- validate (or, if mining, determine) transactions;
- apply rewards;
- verify (or, if mining, compute a valid) state and block nonce.