It can do, certainly I've had transactions rejected where the databox in the Payment Gateway has filled automatically with my initial rather then my full name and once I put my full name in the 2nd time it's gone through
Banks will check that the relevant IBANS are valid (Not necessarily correct for the name on the recipients account, purely that it is a valid IBAN), that there are no flags on the accounts and quite often they run additional post transaction checks on higher value transactions as well after the transaction has posted so it could still be reversed.
Some of the algorithims they use are easily available online, Mod 10 and Mod 11 checks are just an equation of the sortcode and account number that if it gives a certain answer, it's considered valid. Value limits are usually not available and depend on a banks risk appetite. However, and to give a simple example, if you use a debit card on London underground, once you tap and go, the bank in question has a set time period to send an ack/nack message back. (15 minutes I think). If they reject the transaction, you will be allowed to leave the station you get off on, but the card is then blocked and cant be used again. So it also depends on the nature of the transaction as well.