If it is gummed up, synthetic may cause leaks and may also cause sludge to be dislodged blocking oil passageways or even the pick up tube leading to other issues beyond leaks. My normal way it to switch to synthetic and change the filter at short intervals and continue to do so until the filter is no longer "heavy" (you will be able to tell). If it looks really gummed up, I would be tempted to let it idle with a quart of ATF mixed in with the old oil for ~10-15min (or more) while hot before I changed the oil to synthetic. While I would normally change the filter at 1000 miles in the case of a synthetic switch over, I would be tempted to change at 500 miles if it was gummed up. However, the early changes are only to remove the sludge and build up that accumulate in the filter, not help with leaks. Frankly, I think the leak thing is over blown, I would be much more concerned with sludge being dislodged and causing other issues. In my view, if all that is holding the oil in is sludge and low oil pressure, then you have issues that are beyond redress with any oil.
*not legal advice*