That is still a month away. Even though it is pretty much all snow covered right now, I am pretty sure the trail and pass will be free of snow, or nearly so by early July.
A few patches of snow along the way should not be a problem to anyone.
Went up to the pass over the weekend and on up to Mt Gould.
A lot of snow in the trail and many of the switchbacks are covered but we made it fairly easy with just hiking poles. Crampons were not required because the weather was warm and the snow slushy....