There are two questions here: 1) is it "inappropriate" for the OP and son to co-sleep with the boyfriend, and 2) is it inadvisable to do so for legal reasons?
The second question: there are many posters here who have experience with the courts and are saying it's inadvisable since some courts may take issue with it. I accept that.
But as for the first question--is in inappropriate--I'm going to say not necessarily! Why is sleep suddenly so sacred? What it is about sleeping that makes it horrifyingly inappropriate for anyone but "bio-parents" to do it with their children? (Never mind that there are lots of adoptive parents happily sleeping with their kids.) The boyfriend is around during the day and surely interacts kindly with the child while the child is actually awake. It's perfectly appropriate for the boyfriend to, say, pick up the child when he cries or hurts himself, or share meals with the child, or play games with him, sing songs with him, watch movies with him, etc. Why would sleeping with him be held to a different standard?
My husband and I work a lot of nights, so my son often falls asleep snuggling with his grandma or the babysitter. He naps mostly with me, but if one of my friends is over and wants to snuggle with him instead, I welcome the break! It never occurred to me that it would be considered inappropriate for him to sleep beside anyone who isn't me or my husband, as some have suggested here. But I guess I don't view sleeping with the same reverence as some of you do.