I assume you are talking about changing the color of a wrap that is already installed. If so I would think it would be hard to get a consistent, and/or, consistent color and amount of penetration if for no other reason than just considering that there is a certain amount of glue absorbed in the linen when it was originally installed.
All that said, unless there is some reason to preserve the original wrap on the cue at all costs, well then just try it. At worst it's $5 worth of linen and 30 minutes or so to rewrap it with your preferred color if it doesn't work out. I would think dying the new linen before installing would yield a much better result, but like I said, it's a cheap experimint.