If you mention your current job in CSS-2013 Exam Form then they will ask for Departmental Permission/N.O.C, through proper channel not only give you pay protection but also its a clearance from your department that if you are selected then will be relieved. If you don't require age relaxation then you can conceal this job by not mentioning in the form.
Furthermore, if you want to prove that you are working here then mention it in application form, before written exam or even in some cases after written exam FPSC ask for N.O.C. So you have ample time to persuade your boss.
BTW your boss can't stop you to achieve your dreams legally.