It's likely that the additives we discussed earlier will begin to lubricate the seals causing them to become more flexible and leading to seal swell which may plug those gaps over time. The only drawback is that there's no way of knowing how long it may take for this to occur or if the seals are already too far gone to be salvaged. If the problem doesn't correct itself, it is likely that the seals and gaskets would have to be replaced to prevent further oil leakage. So, to wrap up. Petroleum oils can screw up your seals and gaskets and then fill the holes with gunk and deposits to cover their tracks.
Synthetic oils come in and begin to clean up the place.
The odds are definitely in your favor. As is the case with most things, you tend to hear much more about the horror stories than you do about the success stories. I have spoken with numerous people who have made the switch successfully without ever having a leak. In fact, I personally have converted two older vehicles without even a hint of a problem. Just take it with a grain of salt and you and your car will be fine.