If the college you are applying is Private, then producing the category may not be helpful to secure the job. The sole thing required is the ability of teaching which will be judged through the Personal Interview. While applying if its required your category status, then you may need to provide the OBC NCL certificate, otherwise there is not much of a need. If your application form requires to mention your category, then keeping a valid OBC-NCL certificate will be helpful.

I hope this answer provides you some insight. Wish you a  great eve!