Yes, not selecting the sports quota reservation option during the TS EAMCET application might affect your chances of getting a seat through the sports quota in counselling.

Seats under the sports quota are limited and considered during a separate phase of counselling. By not selecting the option, your application wouldn't be included in the pool for sports quota seats.

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

I hope it helps!