As a rule any work (no matter if you get paid or not) must be deducted from your
unemployment benefits (I assume that when you say support your mean unemployment benefits?).
It is because when you get Unemployment benefits you should be ready to take a job at any time (this is the rule about being available).
You will not be available if you have (unpaid) internship.
But some kind of voluntary work you can have and at the same time get full Unemployment Benefits.
We will strongly advice you to ask your "A-kasse". If you are not yet a member you can apply for membership already now. It will be free of cost for you as long as you have not finished study.
When you are member, you can ask your A-kasse what your situation will be if you get unpaid
Our website www.a-kasser.dk should be seen more as a price comparison website and a guide to choose "A-kasse".
Your question require some special knowledge that we dont have, therefore we recommend that you talk with your A-kasse (when you become member).