No, your son most likely won't be disqualified for bringing the online application form home after the TS EAPCET exam.The online application form is usually submitted electronically during the registration process. It's unlikely the form needs to be physically submitted at the exam hall.The focus during exams is usually on the admit card or hall ticket, which contains details for verification and exam entry.

https://engineering.careers360.com/download/ebooks/ts-eamcet-complete-guide-telugu

I hope it helps !