Yes you can study to become pilot even after doing BTech in civil engineering. There are many people in India changing their field to civil aviation pilot. You don't need to have any prior knowledge but the course for becoming a pilot is tough and requires a dedicated study to complete your credits and obtain your certification to fly. Considering fighter pilot, most probably your age for applying for it will be over by the time you complete engineering and thus you cannot become a fighter pilot after that.
To answer directly, civil pilot Yes fighter pilot NO. There is a live example in the form of Flying beast a.k.a Gaurav Taneja who did civil engineering from IIT before becoming pilot in Indigo and now in Air Asia.