Short answer: No.
Capitalist liberal democracies have a very specific organization, and it has been shown that their institutions actually function to reproduce the capitalist system in important ways. The whole apparatus of taxation and the services it provides (police, healthcare, roads, highways, schools) all reproduce the necessary conditions for capitalism in various ways. Schools create a hierarchicalized environment where students are increasingly evaluated and trained so that they will be useful for the capitalist workforce. This helps sustain control and conformity as well as create a workforce ready for capitalist exploitation.
Many of the other services provided by government function in similar ways. I think part of the difficulty of thinking about the problem of anarcho-communism is that it gets lumped in with other 'political philosophies' and we consider them all in the same way. Political philosophy tends to assume that a system of organization is going to be implemented by government, usually in a top-down way. This is what I would call hegemonic thinking. To simplify a little, hegemony is a word for the dominance of a particular system of thought or government. So thinking about anarcho-communism hegemonically means thinking about what it would mean for anarcho-communism to become hegemonic (dominant) in the way our society functions. This doesn't really mesh with anarcho-communism.
Anarchism has often dedicated to pointing out the ways in which government and capitalism are linked and help to reproduce each other. Anarchism has always been a counter-hegemonic movement, meaning that it struggles to point out the problems with any hegemonic system. It struggled against state communism in the USSR and it continues to struggle against neoliberal capitalism today. This means that it's often problematic to think about anarchism (or anarcho-communism) in a way that assumes it will all-of-a-sudden be implemented in one country or another. Thinking in terms of 'all-of-a-sudden' presupposes a revolution (violent or not) which I don't think is very useful for contemporary society, especially in the overdeveloped West. Most people are attached to capitalism and government. Anarchism, by contrast, requires the willing participation and cooperation of people. It can't be imposed like capitalism or state communism. This means that it's often more productive to think about how anarchism can be mobilized at a smaller scale to chip away at (or present small-scale alternatives to) existing systems of domination, including capitalism and government, as well as racism, sexism, classism, heterosexism, etc