Sure there will be performance and life benefits, but you won't live long enough to see the life gains, and you won't be able to feel the reduction in friction. I wouldn't use it because with the old seals on your car, synthetic oils might start a leak.
I use synthetic engine oil, gear oil, grease in all of my vehicles. In cold weather the viscosity does not change so the oil will recirculate faster than dinosaur oil. This could reduce the normal wear during start-up. Less friction means more ET at the race track if your into that kind of thing. As far as increased leaks go it does seep faster than dinosaur oil so gaskets and seals need to be in good shape. It does not turn black as fast as dino oil does.