On the loan? No. There may be other requirements that loan account statements be sent, however. For example, mortgage servicers who aren't exempt have to provide a periodic statement to their mortgage loan borrowers even if they have signed up for auto-pay.
On the deposit account side, the auto-pay is a form of EFT that will mean that the bank holding the deposit account will need to provide a quarterly statement at minimum, plus a monthly statement in any month in which one of the auto-pay debits hits the account. But if the deposit account is held by the same institution holding or servicing the loan account, the transfers won't be considered EFTs subject to Regulation E (aside from the prohibition on mandatory use of electronic transfers as a condition of credit), so they won't, by themselves, create a statement requirement.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8