I'd say it is extremely unlikely, given there is no evidence to really even make that connection in the first place. The woman caught in adultery is highly ambigious, so there's no detail we have to say the two are one in the same.
There is nothing in Scripture that says Mary was an adulteress, a common misconception. The only thing we know of Mary's past life is that she had seven demons removed from her . I don't think its reasonable to say that the "seven demons" were the seven types of sins, Mary probably had real demonic possession, though maybe not a literal group of "seven" (since seven is often used symbolically, it may have meant she was thoroughly possessed).
Mary Magdalene is also named many times in the synoptics and is referred to in John 20, though not with the epithet "Magdalene". She was well known enough that if she were the woman in adultery, she most likely would have been identified in the Bible as such. Yes, it is likely that the "Pericope Adulterae" (the account of the woman caught in adultery) is not original to John and that Mary is not called Magdalene in John (but we know this is her based on the other Gospels). Still, this doesn't really give any reasonable idea to say she is the woman in adultery.
Personally, I think it is way too speculative to say they are the same. I mean it is possible, but you could say that Luke walked around as a kid in the crowds following Jesus. Its not absolutely impossible, but there's no reason you'd say that is the case. The main argument that they are the same is to say that Mary of Bethany is the same as Mary Magdalene, which is unlikely if not possible.
In Christ, Superdadsuper, Sr. Content and Community Manager (Bible Wiki) 21:08, June 12, 2019 (UTC)