Not really. I can't remember Marx, but Marxists after him have made the distinction between what they call 'bourgeois democracy' and proletarian democracy. Marx was careful not to say that democracy inevitably leads to Socialism, and in fact correctly notes that proletarian movements have been supressed in democracies, such that revolution would be the only possible way.

>The logic here being that, if the criteria by which elected officials get into government is by promising the demos more and more government handouts, then the logical conclusion is that at some point, we'll have transitioned from democracy to communism.

This line of thought is ridiculous. Communism isn't about "handouts", it's got nothing to do with "handouts". More "handouts" doesn't mean Communism. Which people are proposing that Communism is about handouts? I can't imagine that there are intellectuals so misinformed about the aims of Communism such that they think it merely comes about by giving a lot of money away.

>The Austro-anarchists' solution is therefore to nip it in the bud and ensure that society doesn't employ democracy from the onset.

Then the Autro-anarchist position is flawed for the reasons I have stated.