Run the idea by them first absolutely. Even if they don't like it you've lost nothing.
However, if you already start the business, and then they don't like the idea, well then you still have to pay all your monthly business costs and without any revenue either.
I would say put off officially starting your business for as long as possible, or until you are CERTAIN that you will have a reliable revenue stream. Finding out your business idea isn't working after hiring people, leasing an office space, and scrambling to figure out a plan B with bills piling up, isn't a situation you want to find yourself in.
Instead, I would advise you keep working your current job, do your business idea on the side, and don't move into it full time until you are absolutely sure it'll work.