Is a comma followed by 'and' grammatically correct?

As others have commented, this is about punctuation, not grammar. Unlike others have commented, this is no Oxford comma, it's the first in a pair of parenthetical commas. It does not matter which word the parenthetical begins with. This opening comma is only wrong if after the parenthetical there is no accompanying closing comma, but you haven't quoted enough for us to see if that is the case.

Your quote is likely omitting the secondary comma that marks everything from the "and" as a subordinate phrase.

You, and your invited guest, are free to have cake. The cake, and any accompanying ice cream, are not poisoned.