Syn Oil is thinner, (most common weight is 10-30) and if you are running a thicker oil on an older engine you may get leaks. NOT caused by the Syn oil, just the result of a thinner oil leaking through a gasket and surface that didnt seal that well in the first place.
Syn oil holds way more particulate matter in suspension than dino oil, so older dirty-er running engines will benifit.
There is no down side. Next time you go to the track, ask what kind of oil the "big guys" are runnning.
Call some Corvette "engine shops" or "tuners" and ask their choice of oil.
I have taken apart many an abused engine in my short time, and its no comparision, the engines running Syn Oil like Mobil One are easy to tell apart from the dino oil ones.
Lastly - you spent alot of time and dough on your Corvette, whats another 20 bucks for an oil change...its cheap insurance.