Once an action is trued, there really is no accuracy difference between one action or the next. A Surgeon will be no more accurate than a Defiance, Mausingfield, BAT, Tempest, Stiller, AI, a trued Remington, etc. Your barrel will make much more of a difference than an action will. All an action really does is feed a round to the barrel, then extract the round/casing. There are rifles built off of Remington and Savage actions which shoot just as well as builds with custom actions.
However, a custom action can/will be a lot more feature rich than a bone stock action. It will also be potentially more robust/reliable, and feel much nicer than a stock action. I have a GAP rifle with a Defiance action, and it feels way better than a bone stock Remington or Savage action. There is a noticeable difference in quality, which I'm sure most people will appreciate.
Brianma65, I'm sure you will love your action!