>>2050100All good skills to have, but there is minimal cross over bewteen bouldering, tree climbing and high route hiking. It will allow you to be a bit more confident traveling over the more technical terrian, and having a head for heights and exposure will make class 3/4 less uncomfortable which is a bonus!
You say in your OP
>I've got no traditional "backpacking experience thoughWhich is what you need for stuff like the SHR. It's great thing to have your sights set on though and work towards. You'll definitely want to lighten your load for it though.