I highly doubt that. If it's too low, you can file for an abatement and use the appraisal for that. If it's too high, well, that's a mistake by the tax assessor's office. They can't retroactively increase your taxes. You always get a chance to appeal their assessment.
My understanding was that tax assessors did their assessment based upon what the house is... so how many beds/baths, fireplaces, amenities, etc. Thats why when one puts on an extension, for example, taxes go up.
So the assessor has some data. IF (amd I think it’s an if) a new assessment is created, based upon misinformation, that’s fraudulent. Especially if OP provides it knowingly. And especially if the records show that the house is one thing, then the assessment says it’s something less (in terms of what the house IS, not what anyone says it is worth), and then taxes are reduced based upon that.
Simple hypothetical scenario:
Assessor records have house on half an acre, four beds, three baths, a fireplace, two car garage, and valued at $100k.
Updated mortgage assessment shows house on .4 acre, three beds, two baths, no fireplace and one car garage. Different comps, or algorithm assesses that house, a far different house, at $85k. Taxes are adjusted downward based upon that. It’s fraudulent.
We’re not talking disagreement on comps or valuation on a, apples-to-apples comparison of homes. We’re talking about changing taxes on an apples to oranges assessment that OP knows is wrong.
The big IF is still IF the taxes will/would/could be adjusted based upon this assessment. If the answer is no, all of this is moot.