If the bottle of wine has never been opened then no you cannot get food poisoning from the old wine and in fact the older the wine gets the better it actually is.
But open wine that's been open longer than 5 days can go bad and make you sick however it won't be the same sickness as food poisoning but you may have an upset stomach due to the bad wine.
The white vinegar contained in Wine is antimicrobial which kills a lot of the bacteria that could lead to food poisoning.