Yes, it this situation, the initial poster's child would be recieving SSI. As far as I hear (but don't know firsthand) they do follow ups of SSI (and SSDI) recipients but elgiblity for SSI/SSDI are the same, their are impairment listings for children and impariment listings for adults (they are very similar, but ovbiously the childrens listings are lower in weight/height and so on). There are 4 specific ways a child can qualify for SSI, some of which might limit their activities (low PFT's and such) but overall, most children will meet or equal 1 of the SSA impairment listings and still be able to do normal child activities, sports, running, swimming, bike riding, playing with friends. The easiest SSA impariment listing to meet (especially as the child ages) is 1 lung infection every 6 months that requires nebulized antimicrobial medications (Tobi or colistin). Many CFers have lung infections more frequent than every 6 months, and are still very able to do normal activities.
It seems your concern/curiosity was that this child (or others) would be deprived of activities because they were recieving SSI???? Unless of course the child is VERY ill and really can't participate because of their health, they are "allowed" to carry out all normal childhood activities regardless of their SSI elgibility.
Hope that makes a bit more sense and helps you understand. And I can't speak for the inital poster, but I took no offense to your questions, it just seems that you were interested in some clairification and didn't understand how the "system" works so you just wanted some answers... hope I helped!