I don't think its just TNT, but I'm sure it helped. For years the Braves had basically the entire South. There were no teams east of the Mississippi and below the mason Dixon line. Florida teams would not arrive until the 90s
I remember watching Cubs games on WGN, especially during the summer when school was out and they frequently played day games - they actually had all day games up until 1988 but even after that they were frequently day games more often than not from what i remember. I liked some of their players (Maddux, Dawson, Dunston, etc.) but never really became a big Cubs fan.