Brake rotors

Absolutely. That is a standard procedure as long as they are above the published minimum thickness. There will always be grooves worn into the friction surfaces. It can takes weeks and hundreds of miles before the new linings will wear down to match the rotor surface. Until that happens they won't be making full contact. That means you have to press harder on the brake pedal to stop. That can lead to excessive heat buildup and one form of brake fade. Even with machined rotors you will have less than full stopping power for a few hundred miles.

If the rotors are worn down to the "machine to" spec. They must be replaced. No machine shop will turn them beyond that point. Insurance investigators and lawyers love to find things like under-size rotors and evidence of do-it-yourselfer repairs, especially to brake systems. It's real easy to convince a jury that you were partially at fault for a crash when it was the other guy who ran the red light. They'll argue that you had a reduced ability to avoid the crash.