No, you're off by 180 degrees. The college coaches would love to give these kids a chance. It's the clipped-hair mean-faced women who have been promoted into positions of power in the athletic departments who make them say "No!".
Thinking someone working out in a "gym" is going to be noticed and given a scholarship is absurd. That's like saying someone doing his homework in the library might get noticed and offered an academic scholarship.
In general, spending one's time diligently in the library does get noticed. Perhaps not with a scholarship offer, but with a higher GPA which would lead to greater economic opportunities upon graduation.
It is notable that you're more concerned about scholarship money than actual sport participation. MANY collegiate athletes participate without such compensation. In fact, of the roughly 355K students who participated in NCAA sports last year, over 136K were at Division III schools which do not offer athletic scholarships.