I don't believe. There's a big .410 "kick/fad" going on right now.
Also; IMO the .410 is an "expert" shotgun. Not a big fan of a .410 for youth (even the new "turkey guns") and especially giving a kid a 20ga for supposed "reduced recoil": Look at rifles on various sites; the same model in .308 will weigh a bit less than a .22/250. (sorry--same example opposite problem--smaller gauge guns tend to weigh less thus negating any less felt recoil IMHO)
I killed my first squirrel with a Savage/Stevens 20ga single bbl. It gave me a swollen jaw and a tender shoulder for two days: I thought it was cool.
Dad's M12 16ga is as "brutal" as the Seven while his M37 12ga (even with a decent comb drop) is very tolerable. IMO kids should start with an airgun, .22 rifle and
12ga with appropriate loads and sized guns. Bore doesn't necessarily equate to recoil IMO/E.
IMHO a gun/ammo company would do well with some 28ga innovation: It's a neat little bitch yet not as sexy as a 16: Model 37
Win pictured below:
That is all: