After a transaction has been sent to the Post Transaction endpoint and it returns a successful response:
A successful response (i.e. any response with a successful HTTP response code) indicates that the transaction was successful and has been included into the ledger.
Does that mean it is has completed all the lifecycle steps? And as such there is no need to track it a way or an another.
Note: I'm wondering this comparing to the Etherum blockchain where there is a two step process: submit the transaction, wait for it to propagate.
So the question here asked differently is: does Horizon wait for the whole lifecycle to complete before returning ?