I'm sure it will, because now that the Oregon law has been upheld other states will likely pass similar laws. And at 6-3, even if (presumably) Alito votes the other way it's still a 5-4 vote.
I am glad it was upheld. Every time I think of this issue I think of my mother in her end stages of cancer/chemo. If she had wanted to end her suffering, I don't think there would have been anything we, her family, wouldn't have done to make it happen. We afford, nay INSIST, on that option for our pets and think it cruel to allow them to suffer unnecessarily when the end is inevitable. And yet, when a human is in the same position and expresses a desire to end their own suffering, somehow that's shameful and wrong.