If you want to mod it in, sure.
Given that not only none of her neighbors would support such a move, but that Hitler and the Nazis didn't even like the A-H monarchy, I don't see how it could be pulled off without some kind of free stuff given to Austria (or Hungary, if you went that route).
I also don't think it would be a good idea to give cores to either Hungary or Austria that cover the entire pre-WWI empire. (Claims, perhaps, but at what cost?) And even if Austria or Hungary managed to somehow conquer to pre-WWI borders, there should be plenty of unrest to deal with. Things were bad enough in either country without adding a bunch of newly conquered nationalistic groups of people who hate the government.
Please read what I wrote. I am not about to argue about Austria given free stuff to reinstitute Austria-Hungary. I am takling about the Austrian government calling the claimant to head an Austrian monarchy, something that is not far-fetched historically at all. Austria had one ally at that time, Italy, which was rapidly turning into the weak part of the German-Italian alliance, not providing a shield from Hitler for very much longer. (If I recall history lessons correctly, when Hitler had his amry much on the German-Austrian border, Mussolini had his on the Austrian-Italian border in response, keeping him in check for some time, but that was before Abyssina.) So there is really not much to say about what the neighbours would support. Also, if the neighbours don't support a move, they have all the tool disapproving neighbours have in HoI. And please don't try to tell me that there are no nations in HoI whose neighbours would never have supported their respective fantasy Fascist/Communist/Democratic choices. All I'm saying is, Austria should have the option not only to turn fascist or socialist, but also to turn into a monarchy; quite probably the same is true for some other nations as well, I just happen to know that the Austrian government was actually taking steps in that direction one year before the Anschluss.
And as for how viable conquering the borders of the old Empire is, sure there should be nationalism, unrest and so on. But the same is true if Fascist Austria tries to pull that off. Or D9l Hungary. Or any other nation for that matter.
And the Austrian government precisely considered restoration as a defensive action, trying to provide for a regime that would be viewed as legitimate even by the left, not as something to please the Nazis with.
Of course, if playing as Austria there simply is no way of surviving the Anschluss plans, this whole discussion is rather silly. On the other hand, giving the player a way of restoring the monarchy might be a tool to do exactly that.