No, trusts, corporations, etc are not individuals and so are not required to submit prints, photos, or CLEO sign-off.
However, the person who takes possession of the NFA firearm from the dealer on behalf of the trust, corp, whatever, must fill out a 4473 and pass a NICS check.
This is a new stated requirement. I know of some dealers who have done this, but it was uncommon apparently. Now, it is required.
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