I believe at one point Hermione's parents are mentioned standing on the Platform, so they can get through the barrier. I do think they would require assistance, though. Muggles might need to hold hands with a wizard/witch and get pulled through, otherwise they would just smack into the wall if they tried it by themselves.
Tim the Enchanter
Platform 9 3/4
Can a muggle, but a parent of a witch/wizard, get through the barrier between Platforms nine and ten?
For example, would Hermione's parents be able to help her onto the Hogwarts Express?
Tim's right; Hermione's parents are mentioned on the platform, as are Lily's, I think. I could be wrong, but doesn't one of the books mentions a wizened old guard on the magical side of the platform? Perhaps one of his jobs is to escort Muggle parents and siblings through. I do think they'd require some sort of magical assistance.
I couldn't remember the books talking about muggles on the Platform, but now that you mentioned it I do remember Hermione's parents and Lily's -- thats when we learn about petunia's letter to Dumbledore I think.
Very interesting idea about them having some sort of magical assistance to get through. That makes a lot of sense. Thanks so much for your thoughts!!