Well, I do remember that in the Chamber of Secrets, Hermione's parents were in Diagon Alley with her. That clears the air around muggle-born students' parents being able to be in the magical world.
And remember how in the same book,
Dobby sealed the opening!
Maybe it has a special opening for muggle parents?
There's probably some kind of way that muggle parents are granted a special permission so that they are able to go with their children.
Also, the seventh book talks about
Lily and Petunia having an argument on Platform 9 3/4 (in Snape's memories).
Petunia is a Muggle, yet she was on the Platform! Lily and Petunia's parents are also mentioned later.
So yes, it is possible, but I think you may have to go through with a witch or wizard if you are a Muggle. There must be some restrictions, otherwise muggles would have discovered the Platform by now!