With Spring can I make an optional path variable?

You can’t have optional path variables, but you can have two controller methods which call the same service code:

@RequestMapping(value = "/json/{type}", method = RequestMethod.GET)
public @ResponseBody TestBean typedTestBean(
        HttpServletRequest req,
        @PathVariable String type,
        @RequestParam("track") String track) {
    return getTestBean(type);
}

@RequestMapping(value = "/json", method = RequestMethod.GET)
public @ResponseBody TestBean testBean(
        HttpServletRequest req,
        @RequestParam("track") String track) {
    return getTestBean();
}