Answer:
Citizen's Bank's deposit agreement said, "All deposits are subject to verification" and it had a similar practice. The CFPB did not take too kindly to it and it cost the bank $18.5 million.
https://www.consumerfinance.gov/abo...-failing-to-credit-full-deposit-am...
Your disclosures had best very clearly describe your practices, but I'm not sure the time savings of adopting such a practice would be adequate to cover the compliance and legal risk you'd be accepting.