Depends completely on the restaurant and how flexible you are on the time.
If you want something specific, make PS. Even if it isn't the most popular restaurant in the World - who knows, the stars could align.
If you are willing to be flexible, try new things, or eat at off times, you certainly won't starve.
But yes, we've done it. With varying degrees of success. Our President's Week was not nearly as successful as Eeyore2Us (we got 2 out of 4 short notice PSs), but we were traveling with two small kids and needed to eat on a schedule.