AFAIK, there is no clear uniform opinion regarding GAs plans in the 30YW. In what I read, the authors’ opinions are varying in a wide range including: him being a selfless defender of a Protestant faith against Hapsburg oppression, him trying to create a Protestant version of the HRE with him as an emperor, him just trying to secure strategically important pieces of the German territory to turn Baltic into the Swedish Lake, him not having any clear political idea and fighting for the fighting (and looting sake) and I probably missed few more. And after his death figuring out the goals is even more difficult.certainly such an agreement would obviously have as a basic requirement, that Sweden ceases to be an ally of France and the minor German princes, with the former not being very happy about this, because it means that the imperials can now focus more on it, but leaving this detail aside, it would be interesting to see how this greater Swedish interest in the politics of the Reich could develop later, in particular if the Habsburgs, in the event of a very important victory in the war, used another idea of theirs ( also very difficult to be able to apply Otl, except with a previous modification during the Peace of Augsburg ), i.e. to create special areas where Protestantism is recognized and tolerated ( in practice confining it to certain regions, mainly if possible in the possessions of electors or foreign princes ) therefore we will have a surplus of people moving towards the Swedish possessions in the north, increasing the population exponentially ( of course the same would happen to the Danish dominions in the HRE, in Saxony and in Brandenburg ) but this raises two further questions how religion would develop Lutheran, if its major exponents can be counted on the fingers of one hand, and geographically very close to each other, we will still see a push towards the strengthening of princely power or a greater search for cooperation / integration at an interstate level, the religious fragmentation of Will OTL still be so present or will greater state control contain it ?
So, unless there is a reasonable consensus on what he and after him Oxenstierna had in mind, it is rather difficult to figure a long-term survival model. “Protestant Empire” is seemingly the most reliable long-term solution but it implies a willing cooperation of the German Protestant rulers and GA tended to use the methods which tended to produce an opposite reaction even in a rather short range and his military successors tended to act as the plain and rather indiscriminate looters.
Purely territorial acquisitions model close to OTL is rather shaky: no matter how you slice and dice it, Sweden did not have enough population to provide a big Swedish demographic presence on the German and Baltic territories (something like the Russian imperial model) and its financial situation hardly would improve to a degree allowing to play a role of the best master possible. So sooner or later the system was almost doomed to crush. If not Prussia, and Russia then it would be somebody else but as far as the Baltic provinces are involved, it probably will be Russia: the consistent attempts to get them go back to at least Ivan IV, disparity of the resources is obvious and idea that the Russian state will freeze its development is not too realistic.
There can be scenarios under which a compromise and cooperation are achieved thus saving most of the Baltic territories but they are not very realistic and GA did everything in his power for them not to happen.