No, I don't; synthetic does burn. If you doubt me, put some synthetic oil on your charcoal before you fire up your grill.
Both synthetic and conventional oil start in the ground. Both are refined but synthetic is also distilled, purified and broken down into its basic molecules. This process removes more impurities from the crude oil in the process of becoming synthetic but some impurities remain. Crud build up on the top a piston is the result of a mixture of oil mist/vapor, un-combusted fuel and moisture being vented into the intake, hitting the top of a hot piston and "baking" on; not just carbon. One would have to do a real world comparison between two identical motor to say for sure, but I expect while the crud build up on a piston might take a bit longer with synthetic oil, it will build up none the less.
BTW, the MoCo has finally seen the light and the new M8 motor does not vent head breathers into the intake......:icon_wink: