According to the paylimit scheme you have right to work fulltime and reside in Denmark. Therefor you can also sign up with an A-kasse.
However you should be aware that you only can have benefits from your A-kasse if you loose your job, and if you loose your job you will maybe not have right to stay in Denmark anymore. If your residence permit is connected to the job you have now, then you must leave Denmark if you loose your current job.
And if you have to leave Denmark you can not take advantage of your Unemployment Insurance (A-kasse membership).
So it depends on your own feeling about your future job status, and the possibility to keep your residence/working permit. If you think you can so, it makes sense to pay for A-kasse, if not it makes no sense to pay for A-kasse.
Hope this help.