Sometimes switching to synthetic will cause leaks, but that is typical of older american cars that use cork and paper gaskets. The old gaskets crack and seep. Most of the cracks get filled with gunk, then running synthetic cleans out the gunk causing leaks.
I switched to synthetic on an 87 Olds with 60k and it leaked horribly, but I switched to synthetic on a BMW with over 200k and never leaked a drop.