My understanding is the wood will get brownish over time, rather than the nice shade of red you see on a fresh cut. The dye you put on there is going to blend with the underlying color, but it's not going to change. But, when the wood changes, the mix is going to as well. You'll probably end up with a browner shade of red, I would guess.
They do make UV protective finishes for a variety of outdoor uses, and some of them are clear and hard. I wrote some control software for a paint line many years ago that was used to coat the Lexan lenses many cars have now in place of sealed-beam headlamps. Keeps 'em from getting fogged and crazed. So, I know you can get what you need, if you want to spray a protective clear coat over your finish. But, I don't know what it's called or where to get it. I imagine Google would be your friend there.
But, in any event, I don't see any downside to dyeing the wood. It's not like the wood won't take it or something.