Geneva's independence has absolutely nothing to do with the Swiss Conquest of the Vaud. The earliest territory emerged when the population of the city of Geneva threw out the Prince-Bishop (though he retained substantial territories until the Vaud conquest) in 1526 by signing an protection agreement (which they were able to do thanks to the granting of substantial rights in a charter of 1387) with Bern and Fribourg. The main change in 1536 was to provide a land link to the city, and to transfer the lands of the Prince-Bishop to the city. Indeed, the city didn't actually declare for the reformist movements until after the Duke had been fully thrown out in 1533 and the Bernese conquest of the Vaud in 1536.
So the most likely course is the following:
1526- the city of Geneva, tired of the House of Savoy attempting to use their monopoly over the position of Prince-Bishop, throws him out and signs a protection agreement with Bern and Fribourg.
1533- The Duke of Savoy has been decisively repulsed and the Savoyard Bishop expelled from the seat.
1536- Sans conquest of the Vaud, Geneva remains a relative haven for reformists, but officially Catholic in doctrine.
I would think though that conflict in the area would be inevitable. Savoy will want to put her choice of Bishop back in place, but I think it likely that having done it twice, Geneva won't fail a third time, and so you might see a genuinely independent Prince-Bishop of Geneva joining as an associate at a later date (a la Saint-Gallen or Basle). The Vaud could easily be taken later, or it may remain with Savoy up until a war with France. Whether Geneva can really be called the Protestant Rome in this scenario is much more uncertain, but it seems likely to be inclined to harbour reformists- and potentially go down an Anglican route- at the very least.