IMO, no. If you read Amex’s site carefully under benefits for lounge access, for virgin lounge it clearly states that it’s “available for primary card holder and guest traveling together”. Whereas other lounge access such as priority pass, Amex lounges and Delta lounges it states “available for primary card holder and one supplementary card holder with guest”.
I guess VA lounge staff can’t tell the difference in number, but I’m not sure if they’ll swipe the card (so charge the admission to Amex) just like priority pass with other lounges. If they need to swipe the card, then it’s easy for Amex to encode something in the supplementary card as not valid for entry to VA lounge. But if all they need is take a quick glimpse at the card like QC (which you can argue that my wife can use my card as I’ve never seen any QC staff actually checked the name on the card and ID me before entering QC) then supplementary card might be able to enter, but that doesn’t mean the official position of Amex is “yes”.
I don’t have a platinum charge card so the above analysis is purely speculative based on what I can read. I’m happy to be proven wrong if anyone else has different experience.