No, really. Our equivalent is much less hyped and attended and players are rarely university or college students. Most don't have any HS degree and are "international" or at least "inter-city player".
I think you missed the basis of comparison. In the US, the role of local sports team is largely filled by scholastic sports programs - i.e. small towns in the US turn out on Friday nights to root for the local high school football (American) team in 8000 seat stadiums in part because there are no significant second and third and fourth division professional sports teams.
The public land grant universities tend to fill a similar role at the regional level due to the geographic expanse of the US relative to European countries - e.g. Alabama is about the size of England as a catchment area.
It might be argued that the US minor league baseball system maps onto the European football pyramid model - but it is probably a mistake. Unlike the lower tiers of the footballing pyramid which tend to consist of independent teams which sell players on for profit, minor league baseball consists almost entirely of developmental teams affiliated with major league franchises and have their rosters and lineups and substitution patterns dictated from above rather than in the interest of points on the scoreboard or standings.