That would look pretty goofy IMO.
I'll add cheesy too IMHO.
You'see stuff like that on Rondevous and modern Mountain Man guns. Originals....nope, and you'll see a lot stuff tacked on originals.
Which Bean ?
http://americanlongrifles.org/forum/index.php?topic=15464.0 Early Bean...William 1770s
No known Rifle is known to exist as far as I know. He likely was a rifle builder, but maybe not prolific since he would have been busy dodging Cherokee arrows . The rifle would be "early" research the Old Holston Rifle.
Mid Bean...Jesse, Russel 1790-1820
Some of these may be around. The rifles would look or should look like the work of a early John Bull.
The Kennedys, Beans, Bulls, Thomas Simpson, Mathew Gillespie, Jacob Young and the Humbles of Kentucky were active in this period. I know this covers a large area NC to Kentucky to the Cumbeland to East TN to SW-Western Virginia. These types of rifles are the bridge from the earlier Colonial style to the later Southern Mountain style. Sorta
The Beans and Bulls were linked by marriage. The Indian Fighting Russels are linked to these families as well.
A rifle from this period may have a stepped toe SW-VA-KY-Cumberland feature, may be in brass or iron, some may not have butt plates....some have heel, and toe plates but no actual butt plates....
Basically if you were going to build a rifle in 50 caliber and without a buttplate I would choose this period. This style of rifle lends itself to larger calibers and the butt shape more suited to use with out a plate.....With that said fitting a plate is no big deal but finding a correct iron plate is.
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Late Bean...Baxter 1830
This is what most think of as a Bean Rifle.
These have the deep crescent iron butt, and are in calibers below .45. ....This is the Classic Tennessee. This type of rifle is not really suited for .50 caliber and no buttplate but...you can build what you want.
The easy button would be to contact Dennis Glazener (Gillespie Rifle Works) and get your wood stocked in his 1810 Mathew Gillespie pattern.