As DiFC points out, the answer is: No!

Rrom the mobil-1 website:

"Myth: Mobil 1 will leak out of the seals of older cars.

Mobil 1 does not cause leaks. In fact, new Mobil 1 with SuperSyn™ was tested in dozens of industry standard and OEM tests to prove its seal performance. It is fully compatible with the elastomeric materials from which all automotive seals and gaskets are made.

ExxonMobil engineers are wary of conventional oils that tout their use of additional seal-swelling agents. With extended use, these agents can over-soften engine seals, resulting in leaks. More to the point, an oil additive will not rejuvenate worn or damaged seals. The damaged seal may have been caused by a worn rotating metal component in the engine.

If an older engine is in good condition and does not have oil leaks, Mobil 1 with SuperSyn™ provides the same advantages as when used in a new engine. ExxonMobil recommends taking measures to repair the leaks, then using Mobil 1 with SuperSyn™. ExxonMobil also always recommends following the automobile manufacturer's manual for the proper oil to use. "

Synthetic oil is chemically inert, if anything the seals should last longer with synthetic. It's denied by Mobil-1 and Amsoil, but the reason that some people observe leaks in high mileage engines switched to synthetic oil is probably that the synthetic clears the crud deposited on the seals, and because if flows better than dino-juice at lower temperatures. Not only throughout the motor, but right past any marginal seals. I wouldn't hesitate to use dino-juice in an older motor that has been on a diet of synthetic, but I would be hesitant to begin using synthetic on an older motor raised on dino-juice. I have been experimenting by switching all my lawn and garden equipment to synthetic, no leaks so far, but obviously I'm risking less here than switching an old car.

-Punxsutawney Phil