I've done one of those in the past, and you're right, it does take the dye very well indeed, especially brown. BUT, and it's a big but, all the trim and stitching and velcro etc. will not take the dye at all and you end up looking like one of those Victorian photos of a youngster dressed in clothes that have piping all over. There's a lot of trim on these garments that you don't really see, but trust me you see it all right when it stares out at you from an otherwise greatly improved garment.
I've always meant to try this with both normal dye and a chemical dye at the same time, that'd work but the chemical dyes need boiling and such, and are not the same simple procedure as those for cotton.
I hope someone will come along with a solution for this, as I've quite a bit of kit I can't wear for this very reason.