First off, conference tournament games are included in the conference record on all the reports used by the Selection Committee and the records don't differentiate between the regular season and the conference tournament.
Second, I don't think A&M make the post season in 2013 without winning a couple of SEC tournament games. Our RPI was in the 40s but we got it up to 34 on selection day. That's still, by far, the worst RPI for a 13 regular season win SEC team that's gotten into the NCAA tournament since we joined the conference.
Third, a more recent example of an SEC team playing its way into hosting a regional---2019 Ole Miss, who went into the SEC tournament 16-14 in the SEC and with an RPI 26. Virtually no chance to host at that point. But they went to the SEC Tournament final, improved their RPI to 22, and hosted.
Fourth, winning the tournament definitely helps you out beyond auto-bids. See 2014...LSU and TCU played their way into national seeds by winning their respective conference tournaments.