Probably, but it depends where you go (especially how high you go).
There's often a little bit of left over snow in July on the Oregon PCT, so there will just be more of it at the end of the year. You might want to
see the snow conditions in this 11 minute slideshow from Oregon in late July. It was a heavy snow year, but since you'll be going in the end of May, you'll see much more snow, even in a light snow year. (Sorry that the video is a bit slow, but I use it in my PCT presentations, so I'm talking over the video. Without my narration, it is a bit slow and boring!)
Check with
postholer a week before you go, but it's quite likely that you will see a good amount of snow, especially around the Jefferson Park, Mt. Hood, the 3 Sisters, and Crater Lake.
It will be passable, but get ready for lots of postholing. Consider snow shoes, although I wouldn't bring them. However, I have a lot of patience for postholing, since I walked across Colorado in May.
My advice: choose the lowest elevation section you can find, make sure you have good navigation skills, and carry lots of patience.
Let me know how it goes!