I took that route with my fifth wheel last summer. Certainly a beast of a hill just outside of Pemberton, my 7.3 was in first gear both up and down for a few parts of it. I am 42 feet long and heavy.
It is a beautiful route, there really is lots of camping, but not many will take a larger rig. Seton Lake BC Hydro site is very popular and can be blistering hot too. We camped there once in 100F temps, the creek was so cold, it's glacier melt, we had to make a shallow rock pool so we could dip for a few seconds at a time.
Alice Lake is a BC Park and will take your rig just fine.