First generation iPad - no protector, no scratches. Wrap-around case? Absolutely yes.
My philosophy is that damage is most likely to happen in transit. In transit, a screen protector is far less protective than a cover (Smart or otherwise). Impact worries me far more than scratches, and with a case, I'm covered for both.
For what it's worth... Yes, a screen protector preserves the oleophobic coating. In fact, the coating never gets used at all. That sounds good if you're planning to sell your device when you're done with it, but I far prefer the feel of the naked screen to any of the screen protectors I've tried. I'm just not the type to sacrifice my own user experience in order to enhance resale value. If I've used a tool so much that the surface finish wears off, then the tool has more than paid for itself.