Marching over the Alps would be pretty disastrous. Just ask Hannibal Barca.
Hannibal had less problems with the Alps than the Roman strategy of avoiding him ...
I am no expert about the 30y-war but if Gabriel Bethlen survives and the Swedish invasion occurs as OTL I could see the Austrian splitting up and loosing in Hungary (maybe little Ottoman help for Gabriel) as well as in Germany. Gustav Adolf's mercenary army takes Bohemia and Bavaria. The latter surrenders, the former goes to Palatinate and helps the Swedes out with troops. Austria is soon taken and Gustav Adolf spends several years in Germany, restructuring the country. Maybe getting parts of Brandenburg and land on the Elbe from his Hohenzollerian family-in-law in exchange of Saxon land (the Elector of Saxony betrayed the protestants in OTL).
Gabriel would probably become king of Hungary and he is also be related to the Hohenzollern trough marriage.
The Swedish land in Germany would probably cover all of the Baltic coast and maybe also areas at the North Sea.
Christina would probably marry a German prince (House Wettin, Hohenzollern or Palatinatian Wittelsbach comes to mind). Their potential child could be heir to two countries and a reason for Gustav Adolf to stay even longer in Germany.
The Habsburg might attempt to retake their homeland and unite the Swedish-German-Hungarian-French Alliance once more ... Germany suffers even more in this scenario. The crown of the empire might go to the french because they helped so much ... but their power is limited to the Rhineland ... Bohemia turns protestant, Bavaria maybe too...
Just my ideas
