In general, No.

There are some places/trains and situations such as disruption where it is allowed or authorised for specific reasons or just not enforced but in general train companies that have mandatory reservations do not want non-reserved passengers on those services.

In most cases these trains have GATEs at entry-which you can only pass with the right piece of paper-or on fone. F.e. €* or most FR TGV or now also in IT for frecce or in ESpana for AVE (plus luggage checks)

This might be possible when seat reservations are optional, such as in certain DB trains. When a seat reservations is required, it is considered mandatory and you might be fined if you're unable to produce proof of reservation upon inspection. 

OK, but does someone prevent you from going into the train ? Without seat reservation while required.

Hamburg-Koebenhavn seems be an impossible journey....

No one prevents you from boarding the train, but you might have to leave the train.

Even on trains with optional resevations people without reservations can have to leave the train if it is too crowded.

I was on a train with optional reservation from Berlin to Prague today. I had a reservation and that was my luck as there was an announcement in Berlin saying that all travellers without reservations had to leave the train. The police came and helped the train crew to remove people without reservation from the train.

You can use local RE train Hamburg-Flensburg, than IC Flensburg-Fredericia and from there IC to Copenhagen. I would suggest to reserve seats for IC Flensburg-Fredericia, but it is optional.