I don't think it would make it worse, but I don't think it would help. The problem isn't that the paint isn't drying, but that the solvents in the paint are reacting with the vinyl. The paint just won't cure completely (or it takes a really, really, long time).
On a related note, some vinyl will even react to the styrene, melting it when they are left touching each other for a while. Strange, but true.
Paul