Not really. When Tennessee was right, it wasn’t just with in-state talent. They’ve always been a factor in Atlanta, the Carolinas, and have even gone up in the Tidewater (Justin Hunter). Middle Tennessee has OK talent but certainly not great.
I think they’ve lost some ground over the years in Memphis, but not necessarily because of Vanderbilt. They’ve lost guys like Barrett Jones and Donta Hightower to Alabama. Back in the 90’s, before Calipari, the Preds, and the Titans, there was one sports team in Tennessee and it was the Vols. Not the case anymore, so wearing the Power T helmet isn’t as prestigious as it once was for kids growing up in the state.
It’s not as easy at Tennessee as it is at Florida, Alabama, or Georgia, but they still have a great talent pool within a fairly small radius. Vanderbilt isn’t the problem.