Well you'll first need to establish under what form the union exists. Sweden and Norway were always minor partners in what was esssentially a very medieval construction, a feudal union of nobles aligning themselves with the danish monarchy.
To continue the Union into the TYW you'll need the danish monarchy to keep their relationship with the swedes stable, not an easy task as we are talking about a union where the largest member, Sweden, is subject to a minor power, Denmark. Given the resources and brilliant leadership that Sweden had compared to Denmark in the period following the union it'll be hard to argue against the dissolution of the union.
What line of kings will the union have? Danish kings in the period you mention, from the Kalmar union till the napoleonic wars, were almost all completely incompetent. If we continue the OTL union being dominated by Denmark then bad leadership will be imminent.
My best bet would be that if the swedish rebellions are kept under control by Christian 2. Sweden grudingly stays in the union. When Christian 4. enters the TYW and attacks the German Imperials from the north he'll probably still squander his army given how horrible a tactician the guy was. The swedes will take this as a nice chance to rebel and the Union is out of the war.
If such a rebellion is put down and the union continues into the napoleonic wars the even more hilariously incompetent Frederik 6. will probably try to maintain armed neutrality. With Sweden and Denmark united the Union has control of the Oresund strait leading into the baltic making the two countries vital in securing English-Russian interests, making them an obvious target. If Frederik is stupid enough (which he is, given his OTL behavior) he will insist on not joining either England or Russia. The English will take on the Union fleet and seperate Denmark from Sweden, and either give an independent Sweden to whoever promises loyalty, be it the Russians or a Swedish king. If the Russians get Sweden they'll gobble up Norway eventually and from there the Union is officially no longer feasible.
If you somehow make the Union a Swedish-dominated power then the sky's the limit. Let's say Margarate 1. marries an important swedish prince and creates a new dynasty. If things go smoothly for the next hundred or so years a very powerful protestant empire will arise in the North. There's still the problem of being between the important German and Russian groups, but if the Kalmar monarchs play their cards cards right they might be able to create a power great enough to prevent the establishment of a central authorithy in either Germany or Russia. Then we might have power struggles between the Nordic, Austrian, English and French Empires in Europe over the next odd hundreds of years.
In the end though I don't believe the Kalmar union will remain a great power. The population is too small and their resources too few in the end, they'd have to rely on Swedish ore to craft most of their weapons for example. In the end a Kalmar Union might at best accomplish what Gustav Adolph did, only a little better due to the few extra resources from Denmark and Norway and the benefit of fewer internal nordic wars.