Synthetic oils have better cleaners and break down slower than conventional oils. Engine seals get 'blown' out because of excess crankcase pressure.

Now, the answer to your question. If the engine is very dirty and the seals are covered in sludge, introducing synthetic will remove the sludge - a good thing. If the sludge has been covering the seals for a very long time, the seals will have 'dried' out from lack of oil and removing the sludge will cause leaks - bad thing. BUT, as the seals start to swell with fresh oil, they will no longer leak.

Pull the oil filler cap and take a look at the cam shafts. They are probably dark brown from oil baked on them. Synthetic oil will get rid of that dark brown color in about 2,000 miles. Your engine will be much happier.
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Keeping it running is better than buying new