I'm going to say no, not unless you have budget to spare and literally nothing else to spend it on, a better processor will always make more difference. Loading / bootup is only small amount of the time you'll spend actually using the machine so not a priority for 'optimizing' I don't get all this wooing over boot times, it's a couple of seconds of your day.
Likewise, better controls are infinitely more important than an SSD
Maybe if you're expecting the cabinet to take a real beating then an SSD might be a better option than an HDD, but many arcade games use regular HDDs now without that being a major concern for the manufacturers.
Otherwise, it's one of the very last things I'd consider allocating budget to.