I don't recall the source, but remember reading that one of the demands or hopes that Hitler had for Austria in the middle thirties was that the Schuschnigg government would allow free elections for a new Austrian parliament. On the surface this is pretty ironic in that we have a dictator insisting on another dictator holding elections, but it makes complete sense. In any new election, the Austrian Nazis were bound to do well, very well.
In the last elections, in April of 1933, for Innsbruck Austria, the Austrian Nazis won a plurality, 41% eating into the support of all non-socialist parties. In previous elections for state parliaments held in 1932, before Hitler took over in Germany, the Austrian Nazis were also on the ascendant, going from negligible numbers to the mid-teens to low 20's in Lower Austria, Vienna, Voralberg and Salzburg.
So, assuming Schuschnigg actually caved to German demands and elections were held, a Nazi plurality victory was quite possible, maybe with support levels in the 30's, and similar but slightly lower numbers going to Schuschnigg's Christian Socials, and the Socialists, so kind of a three way split but with the Nazis as the largest party but nowhere near a majority.
The political ramifications of such an election might see some kind of Nazi/CS coalition, with a new government taking gradual steps toward Anschluss, but without anything too dramatic happening at first. Maybe a customs union, Austrian withdrawal from the League of Nations, and abandonment of the alliance with Mussolini and full scale pro-German stance in foreign policy. Then maybe talk of a national plebiscite for an Anschluss. With a democratically chosen government making such a step, it would probably happen without too much of an uproar from the British and French.
Would the Christian Socials agree to this form of national and political suicide however? I think they'd be even less supportive of working with the Socialists, their only other option, or perhaps they'd try tolerating a Nazi government that has no majority in the parliament and could be in theory be voted out of office at any time with a combined vote of Christian Socials and Socialists. Would a Nazi chancellor like Artur Seyss-Inquart hesitate one moment from entrenching himself in office even without a stable majority backing him in parliament knowing German support is his for the asking.
Regardless of the path, free elections in Austria in the middle 1930's was bound to strengthen the movement toward Anschluss, perhaps bringing it about in a superficially more democratic matter.