I would not call this running the whole PHP application in one transaction, but rather a PHP script that treats each request in a separate transaction.
That is fine, as long as you are aware of transaction related concepts, such as locking, deadlocks, starvation, ... In essence, you should like in any other environment not lock database objects longer than necessary, prefer fine grained row locks over full table locks and protect your database against deadlocks.
But as those same concepts apply in a pure SQL engine based (stored procedure) solution, there is no particular reason not to do this in PHP.