Would it not give them a common cause to rally around to keep fighting?
I'm not sure. I guess I was just think of the context. Ferdinand would be trying to bump up Austria in the 1620s when he's riding high (before the Swedes come knocking). So I think that the Royal crown for Austria would be seen as part of a general overreach on Ferdinand's part.
Interesting. So essentiall an Austrian "secession" from the empire in all but name?
Maybe. It's an in interesting question. I guess it depends upon what Ferdinand was thinking which probably would have been different from what he ultimately would have been able to get away with. If you want to get into the weeds you can look to Bohemia, which is the only real example we have of a Kingdom within the HRE, where a legal argument has been made that the Kingdom of Bohemia was not actually part of the Holy Roman Empire. The argument is that the extensive privileges that accrued to the Crown and Estates of Bohemia, that the Emperor was required to accept as King whomever the estates chose, basically meant the Emperor had no rights over the succession which runs counter to any notion that the King was his vassal. Thus legally the King of Bohemia was only an Imperial vassal in his capacity as Arch Cupbearer an office that the Emperor invested him with as Elector and that office had no territory associated with it. Then you consider administration and justice. Bohemia was not subject to the German Chancellery (the de facto singular Imperial Chancellery since the nominal Chancelleries of Italy and Burgundy didn't exist in practice) as it wasn't part of the Kingdom of Germany. While the other Electors had the privilegium de non appellando that prevented their subjects from appealing to the Reichskammergericht I believe Bohemia had it as right that was not revocable by virtue of its autonomy.
So to bring this back around to Austria and I guess ask the question what would Ferdinand's Kingdom look like you could make the argument that Austria would similarly no longer be a part of the HRE, legally speaking, if it involved removing Austria from the Kingdom of Germany and thus from any association with the German/Imperial Chancellery and the jurisdiction of the Reichskammergericht and granting Austria control over its own internal laws and succession. For the Reichskammergericht, for example, legally this change goes beyond the Privilegium de non appellando since it would no longer be a privileged exemption to a normal jurisdiction but a complete severing of Austria from those institutions. And its permanent meaning future Emperors theoretically couldn't revoke it.
It does raise the question of representation in Reichstag as it would represent a serious reordering of the territories of the Reich. The individual states the Habsburgs, or any dynasty, held still had separate votes based on their traditional rights and status within the Imperial hierarchy. So a single prince could gain votes if he inherited multiple states that each had votes. The Erblande, for example, gave the Habsburgs several votes Princely and Electoral derived from different individual states. Thus states were never de jure combined into a new single legal territorial unit. So raising Austria to a singular Kingdom would be the first time the territories of the Reich had been seriously adjusted in well over 100 years. Which is part of what I thought might arouse the opposition of the Electors or Princes.
So anyways when you compare what Austria could gain in such a scenario vs what it had OTL in practice I don't think the changes are that big. The Erblande were exempt from the religious settlement at Westphalia and as long as the Habsburgs were Emperors they would have a guaranteed privilegium that would give them further legal autonomy. So really the elevation to a Kingdom probably just makes permanent things that were only privilege OTL and makes de jure that which was de facto while broadening the Habsburg powers a little bit more in certain areas. On the other hand it threatens to open a whole pandora's box as the Electors and Princes may demand their own territorial adjustments (in a legal/administrative sense not in terms of ownership) because the act of creating the Kingdom, while arguably having limited practical effects, has pretty huge implications for the legal structure and hierarchy of the HRE.