Nope, they're just bearing a ranged weapon now. The same is true if you put a
Fell Beast on a Nazgul which is already fierce such as
The Witch-King, Lord of Angmar - he won't get two extra skirmishes because there's no such thing as "double fierce," nor "double archer." Keywords without numbers don't stack. However, if Gimli bears
Gimli's Battle Axe, since the Damage +1 keyword is numeric it will add up and give him a total of Damage +2.
Compare
Elven Bow to
Southron Bow. In addition to making the bearer an archer, it can add +1 to the archery total. If bearer is not an archer it effectively adds 2 to the archery total. If bearer is already an archer, it adds 1.