no...CPR number is not mandatory for your rights to receive dagpenge. However you will not be able to use NEM ID to log in to your A-kasse website and Jobnet.dk, which you are obliged to do regulary while receiving dagpenge.
So, I will recommend you to ask your A-kasse and also jobcenter if you need to keep your Cpr. of practical reasons.
Anders Weber, www.a-kasser.dk