Yes. Homeless people who are Danish citizens enjoy the same rights as every other Danish citizen. This has not always been so: a homeless person did not get voting rights until 1961. Also, it was not until 1961 that the restrictions that accompanied allocation of poor relief were rescinded. Until then, help was only given with various civil right restrictions.
It is important to note that not all homeless people in Denmark are Danish citizens, and without a Danish citizenship, it is not possible to vote and thereby influence the political situation of the country you are 'living' in.