Dyeing an FO?

I want to make a felted bag for my school counselor. (her birthday is next week, so I should start soon).
Her favorite color is yellow so i want to make a yellow bag, but I looked in walmart (they have no yellow loin’s wool) and then i went to the closest knitting/craft store and they dont have any good yellow. (I just want a pleasant yellow, like canary or lemon or baby yellow) They only had orange and yellow brown and a kind of dirty-tobacco-yellow. SOOO, I bought some plain wool yarn so that i could dye it at my house.
I know how to dye and i already have my yellow kool-aid, but i dont want to unwind my perfect galway-center-pull-ball and then wind it into a ball again after it is dyed, it’s sooo much work.
So i was wondering if I could just make the bag and then just dye the completed bag.
Would that work?

I think that would work fine, but do it before it’s felted.

If you have enough my suggestion would be to make a small swatch, dye it and then felt it to see how it looks. That way you won’t have gone to all the trouble and find out it really doesn’t look right after felting or it dyes weird or something.