The truth is, this does happen, but you want it to happen less. Banks accept certain amount of risk due to logistical limitations, but always seek ways to reduce it.
Tradeoff between availability and consistency. Not to error when accepting a transaction probably makes bank good money, but showing correct numbers all the time or handling transactions larger than entire account balance probably only ever helps poor people like me who anxiously check incoming transactions at the ATM and we don't make banks lots of money. So a queue of transactions to record doesn't sound like a problem, but idk I don't work at a bank
Accounts go over their overdraft limits all the time. Arranged overdrafts are simply the limit the bank promise to honour without punitive fees, not an absolute limit.
Honestly I have seen enough times purely savings/debit account goes negative a few dollars that what you describe is probably not a show-stopper :) Only if discrepancy is large enough then probably transaction gets flagged and a human steps in.