Add this to "Is global warming real?" and "Would a salary cap help baseball?". Everyone will deliver an opinionated response but there's no end-all answer.

It's my belief that if you want to get faster or stronger on the bike that you should ride your bike to achieve that. I also believe that smart crosstraining for any sport can improve your overall fitness, which in turn reduces your risk for injury, which can increase your training capacity. This especially goes for core strength; if anyone tells you not to waste your time or that it can't help performance, I don't think their research is complete.

The only way to find out is to see how you respond while making small, incremental changes to your workouts. What works for me or anyone else, will almost assuredly deliver a different degree of success for yourself. Just remember to change your routine slowly and listen to your body to prevent injury.