Can you skin over an existing roof deck that is breaking down?
It hard to say without seeing the structure but it sounds like the decking was under engineered for the weight of asphalt shingles to begin with. You could put the OSB overtop but by the time, you clean that surface up (pull nails, etc) and adhere the new surfaces together, you might as well strip it.

You're also leaving extra weight on the roof and if you are already feeling degradation between the rafters, you may ultimately end up with the same problem just thicker.

If you are going to go with asphalt, you might want to upgrade to at least 7/16th OSB depending on your rafter spacing.