Looking through the guidelines at appraisal management and third party arrangements I didn't see anything that that would specifically prevent it.
The AMC would IMO be an independent party and they are responsible for choosing the appraiser. As long as the loan officer cannot in anyway directly or indirectly influence the AMC's choice of appraisers for the assignment I don't see an issue however you should have your procedures for who can and cannot order appraisals documented.
If the loan officers have assigned processors then I personally do not see a need for them to be ordering appraisals.
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The opinions expressed are mine and they are not to be taken as legal advice.