no its not possible. When you cancel membership in an A-kasse, you always need to start all over again, if you later become member again. This means that you need to be member for 1 year before you can apply for unemployment benefits.
And it's nots possible to pay for membership "back in time".
However you are an eu-citizen, so if you have paid to unemployment insurance in another EU-country after you moved from Denmark then you will have the posibility to transfer your earned rights (membership period and registered working hours/income) from the unemployment insurance in the other EU-country to the danish A-kasse.
And because you have been member in a danish A-kasse within the last 5 years, then there will be no other requirements for being able to transfer your rights. You can read more about transfering rights between EU-countries here:
Let me know if you have further comments/questions.
Anders Weber, www.a-kasser.dk