I would not do it unless the vinyl was falling down.
I would not paint over soft vinyl. If you change the vinyl it is a huge job and the type of vinyl and glue is critical. I have done mine twice! The first time was what I was told was a good vinyl but it did not have non-mobile plasticizers. When the deck gets very hot the compounds used to soften the PVC migrate to the glue making it a skicky mess.
What has worked very well even in the tropis here is Naugasoft off white vinyl and 3M spray General Trim Adhesive. The 3M Vinyl and Rubber spray adhesive is harder to use and can eventually stain the off white vinyl. I haven't stuck the vinyl direct but on to white non-piling poly fleece material as a felt backing to give the cushioned appearance of the original but without any foam. Where the translucent parts are in a few small spots with no core near the windows I used thin closed cell foam instead. There are various reasons and tips but it looks great in a light colour.
I am sure there are other ways but the main thing is to not use foam backed vinyl and use quality products as the time taken for the work is substantial. There are some pictures here of Popeye with off-white ceiling.
John, Maramu 91, 1981, Popeye, Australia