I've heard Adam Silver actually talk about the NBA doing something similar, but a little different than what you proposed. No it would not count toward the regular season record.
They are looking at the FA Cup in England for soccer as a model where every team is included in this single knockout tournament where the rounds are just played throughout the year.
That said, I don't think it'll ever happen because I can't imagine many teams putting in any of their good players when they are already holding them out for regular season games.
Probably would never get off the ground, but the idea is not as far-fetched as some seem think.
http://probasketballtalk.nbcsports.com/2014/10/29/adam-silver-talks-about-a-mid-season-tournament-coming-to-the-nba-eventually/