35% is good protein, maybe too high, but also some other important elements may be lacking. You might be able to get away with mixing the spent grains with a turkey starter. You want protein to be about 28 percent for the first few weeks. I would look into the Pearson square, which is a way to calculate protein content of a mixed feed. You will also need to watch lysine content.
I give my laying hens large bins of spent grains from a local brewery (I have over 100 hens and I give them about 100 gallons of spent brewery grains at a time) , but that being said, frequency is about once a month and these are fresh, wet, hot grains right out of the kettle so it might be a different situation as compared to commercially dried spent grains (which is what I'm assuming you're referring to.
I have had negative results feeding *too much* spent grain to my laying flock. Pros and cons. I would say try it, but in moderation first.