I am guessing here... and you would really want to verify this with a person that has a real clue...
But... If you just install the housing (put your semi guts into the FA housing) you should be OK, legally.
From what I have seen all of the lowers came with the FA internals.
YOU COULD NOT BE IN POSSESSION of the FA internals as well as a semi rifle, that would be constructive possession. You probably would also NOT want a paper trail record of you receiving such goodies. As this could be difficult to explain, should there be an issue. The lost the internals in a boating accident may not work.
With all of that said.
I would tell you it's a BAD idea.
If you are just going to mount it in a case and stick it on your wall, fine. But, if you intend to use this gun, take it to a range or have the potential of getting pulled over transporting it, this will be a major headache to explain to every single person that you just wanted it to "look" like the FA version, but it's not REALLY a FA and does not ACTUALLY have the sear (or whatever) installed and it's perfectly legal and ok... no, really.. NO REALLY...
If pulled over... The police will probably arrest, confiscate and let your lawyer explain it all to the judge.
All in all. not worth the headache, explanations and the expense.