it is not the registration of address that is crucial in relation to A-kasse, but instead the fact that you actually stay/live in Denmark.
For being able to get dagpenge you must stay/live in Denmark, because you must be available for the danish labor market, and be able to take any job with one day notice and attend meetings in jobcenter and A-kasse.
If there will be a delay in the processing of your address registration, it will not be a problem in relation to A-kasse, if you just can prove in another way that you actually stay/live in Denmark, for example if you have an tenant-agreement.
It is up to the A-kasse what kind of proof they want from you, so I can not say exactly what is enough to prove that you actually stay in Denmark, but as mentioned an tenant-agreement would be enough.
Before you use the rule about 3 months jobsearch with dagpenge in another EU-country you must meet all the requirements for being eligible for dagpenge, and you must have been registered as unemployed at Jobcenter/Jobnet.dk for at least 1 week if you go to your home-country, or 4 weeks if you go to another EU-country. So, how long you must have stayed in Denmark before you use the 3-month rule depends on what country you go to search for job in.
Anders Weber, www.a-kasser.dk