yeah of course. There wouldn't be any problem but try your level best to let them know about your difficulties before joining as you'll join after the due date is over. Once you put your feet at the Academy then you'll be able to apply for leave, if you'll show them the interview letter then they'll allow you. There wouldn't be any problem, Inshallah. And don't worry about coming to Peshawar as there are two flights operated from Peshawar to Karachi and vice-versa on daily basis, so would be able to reach to Peshawar in just 1 and a half hour. So I'll again advise you not to worry.
Good Luck!

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"Success is not final, failure is not fatal; it is the courage to continue that counts" (Winston Churchill)