"As well as X" vs "As well as X does"

They are both correct, but the first has the potential for a misunderstanding.

"John plays the violin as well as Mary" could be taken to mean (even without a comma after "violin") that Mary plays the violin and John does too.

I could not understand you very well, McTag.

Did you mean it could mean that Mary plays the violin while John just follows suit?
"John plays the violin as well as Mary does" unequivocally points out that both of them are parallel in doing so?

"as well as" can have two meanings (at least!)

1. in addition to

I go to the gym as well as jogging twice a week.

2. equally good as

John plays the violin just as well as his sister does.

Got it.
Cool stuff.