All I can think of for the capacitor use is to stop a high voltage arc and prevent burning contacts when the starter button is released. From EE terms it minimizes the dI/dt (change in current over change in time). Kind of like the old condenser across the points in a distributor on gas engines before electronic ignition. The capacitor should do nothing to help or hurt starting performance.

I haven't seen a Yanmar with a capacitor there. It's not shown in any of the service manual prints.

I'm on my 3rd year with a Walmart Group 24 set of car batteries 650 cranking amps that were $70 each when I bought them. No problems.