Not likely.
Germany still has designs on Austria, and Anschuluss is coming. Now Kurt Schussnigg was kind of a wimp when dealing with Germany--he somehow allowed the likes of Arthur-Seyss Inquart to meet with other Nazis in the government house. Engelbart Dollfuss is certainly a personal friend of Mussolini, but part of Hitler's diplomatic strategy is to befriend Mussolini. In the end, Mussolini would probably concede Austria in exchange for an alliance with Germany.
Now, the Anschluss itself is likely to go down differently. Dollfuss would probably have survived an attempt on his life, and its important to understand that the Nazis were subjecting Austria to a terrorist campaign. Schussnigg caved. Dollfuss might not--and he certainly might go farther to resist Germany. This might make the critical difference--Austria sends its troops to guard the German Border.
Austria's situation is hopeless in 1938, even with Dollfuss as Kanzler. Czechloslovkia might be smart enough to know whats happening, but the Czechs aren't going to be friendly with a nation with claims on its soil. Yugoslavia and Switzerland won't get involved, and Italy is probably disarmed with an alliance and if necessary an outright bribe. The UK and France, even if they hear of skirmishes on the border, are not going to react to this with a war.
Austria is hopelessly compromised internally as well. The Nazis had considerable support in Austria, and this massive 5th column at a minimum would thwart Austrian resistance to Germany's efforts. What would probably happen is that Dollfuss desperately attempts to get foreign support and is stood up by everyone. The Austrian Army, while not totally subverted by the Nazis, is unable to maintain its discipline in the face of the German attack. Small units outright defect to Germany, larger ones face muntinies and other treasonous behavior. No matter the disposition of the Austrian troops, their situation is a desperate one. Dollfuss would probably fight to bitter end, but the Austrian people would not, and Italy grants him one service--an escape route. Ultimate Destination: Argentina.