If the Bank offers a quarterly interest only payment plan for a HELOC, are they still required to provide monthly periodic statements (if there is a balance and/or activity)?

I was under the impression that you must still provide a monthly periodic statement. You might only bill for the accrued interest every quarter, but they would still receive the statement.

Is this correct?

If your billing cycle is quarterly, your periodic statements can be quarterly (but no less frequent). See 1026.5(b)(2).

This is where the frequency comment came from:

1026.2(a)(4): Billing cycle or cycle means the interval between the days or dates of regular periodic statements. These intervals shall be equal and no longer than a quarter of a year. An interval will be considered equal if the number of days in the cycle does not vary more than four days from the regular day or date of the periodic statement.