No, there is a direct relation. At least outside the US, many many children are inspired to go out and try and imitate their favourite sporting heroes, and even if they aren't athletic they usually are included in the larger community and get to play and socialize. This is definitely the case with soccer and cricket.

I haven't seen a single case where being a fan has precluded children from going out and playing.

Perhaps as adults the situation might be different, but their are a whole host of other factors at play there, including health and time issues.