That's pretty much the crux of the whole issue.

We haven't been to a starred restaurant with our kids, but have been to plenty of very nice restaurants with them. On our first trip to France with them, when they were 6 and 8, we got used to the routine: upon entering the restaurant, we'd get "the look" (Oh God. Not only are they Americans, but they have kids!??). Within about 20 minutes, both kids had the waitstaff in the palms of their hands and were treated like royalty.

I wouldn't hesitate to take your kids to Ramsay's restaurant. They'll have a great time.