do you mean a Hemizygous barred hen? hens can only have on copy of sex linked barring gene(B/-) ....Any benefits to mating a homozygous barred RIR to a rhodebar rooster?
let me see if I can read your mind ond ask the correct question....
any benefits of mating a barred RIR out of a RhxRIR cross to a Rhodebar rooster?...
well that mating its called 1st Back Cross to parent(BC1) and the Chicks coming out of that cross are called BC1, this will produce 50% autosexing Rhodebars...(and 50% wheaten/wildtype none autosexing chicks)...
using the chicken calculator(I have one of this calculator on my brain...

parents
chicks...
ANY BENEFITS? well seeing how it only took two generations to get back at Rhodebars from the good type RIR I would expect this Rhodebars to be of a better quality than the original parent(which should have only a distant relation to RIR) this is how the Rhodebar as a breed should be reinvigorated in my humble opinion