The stipulation you have stated is about another employment and the issue is about better educational qualification to improve the skills, and whether part time employees are also covered by Employees Service conditions.
First of all, the institution in the application stipultates occupation while taking admission, if you have filled the same with employee, without such NOC, college can not permit you to take admission. If you have suppressed that information that is another issue.
What is your present issue you are worried about so much ? Disciplinary proceedings against you or if some one cancels your degree because of this internal regulation, though you are qualified and your functioning in your organisation is clean and untained.
What can happen to Degree or employment ?
I have seen a case in Delhi where SI while performing his duty attended LLB and secured the degree and information RTI disclosed that he was permitted only for appearing for the examination, and his attendance was present both in college and Police station, and the complaint to authorities has not yielded any outcome.
To my knowledge seeking such permission is a mere formality and an assurance in writing that you do not neglect your duties during such pursuit of academic qualifications.