I don’t know of anything that would prohibit it from being required. A couple of things you need to consider:
1) Reg E, 1005.10(e), states.. (e) Compulsory use—(1) Credit. No financial institution or other person may condition an extension of credit to a consumer on the consumer’s repayment by preauthorized electronic fund transfers, except for credit extended under an overdraft credit plan or extended to maintain a specified minimum balance in the consumer’s account. This exception does not apply to a covered separate credit feature accessible by a hybrid prepaid-credit card as defined in Regulation Z, 12 CFR 1026.61.
Also, you should consider if this practice would have a disparate impact on your consumers in your area (i.e. is one demographic likely to be denied because they don’t typically have checking accounts) and could that result in a fair lending issue.