I love synthetic in most car/truck engines because of the many advantages it has in those applications, but I never saw a benefit in splash lubricated small engines. Even for snowblowers stored outside, a regular 5w30 conventional is so good that it will pull over fine, and the extra cost of a synthetic 5w30 or 0w30 isn't worth it. Since there are no oil filters on these, changing the oil every season to get the contaminants out will be far more beneficial than using a synthetic vs. conventional.
I've never really believed that synthetic "causes" leaks, but I have experienced increased leaking (note: on engines that are already weeping oil) when using a synthetic in older small engines. This is due to many of them having aged rubber crank seals, and poor sealing paper crankcase gaskets.
I have an older pressure washer with a 5hp Briggs flat head. When using a synthetic 5w30, I have to add a bit of oil every few hours. With a HDEO 15w40 I never have to add any, so any minuscule amount of fuel saved by using a synthetic is outweighed by the need to add oil every so often. Every engine is different, and this one is also several years old with high hours. I tell all my customers that the most important thing with small engines is the oil level, and the change interval, not necessarily the brand/type used.