As the others above say, I don’t think the intent of the C is to prevent you from driving away, but just to inform you the engine coolant is still on the cool side. When the coolant isn’t up to normal temperature the engine computer uses a different algorithm so the fuel mixture is richer than normal. If you really gun the engine in that condition you might risk forcing some raw gasoline vapors past the rings and into the engine oil, which is undesirable for a long engine lifetime.
The engine uses synthetic oil because Honda wanted the car to get good mpg numbers. mpg is an important factor that buyers consider, so it affects car sales. Synthetic oils can be made thinner and slicker and still deliver the needed protection, so friction losses are reduced and mpg is enhanced. Many newer cars require low viscosity synthetic oils these days. Suggest you follow Honda’s advice regarding the oil, as your engine probably uses variable valve timing, which is highly susceptible to expensive problems if using the wrong oil or wrong oil viscosity.