Is the bank able to obtain a signed release from a borrower to obtain information such as tax returns and/ or financial statements from their accountant?

I have an example of such a release that states, "I hereby authorize Bank Name to obtain a copy of my annual tax returns and/ or financial statements along with the tax returns and financial statements of any of my related entities. I also authorize them to receive copies of any supporting information they may from time to time request until otherwise notified."

Is this acceptable?

Are you asking this as the bank or the accountant. If the bank, sure, it's acceptable. If the accountant, it depends on the accountant but I would think it would be fine.

If in doubt, use the IRS Tax Info release form as a guide. If it's good enough for the IRS, it should be good enough for most accountants.