If not, she would certainly sympathize with anarchism, based on her views I do know, which is why I qualified it as "more likely" rather than being certain.
Anarchism may not be a single set of ideas but it's certainly a distinct lineage that descends from certain critiques of capitalism, hierarchy/state power, and Marxism (means-ends unity being essential to the critique of Marxism, eg, that a proletarian state will become oppressive for the same reason any other state becomes oppressive).
For instance, it's broadly held by anarchists that a society should be voluntary and not based on coercion. If someone called themselves an anarchist but was, say, in favor of aggressive policing, I'd wonder what the heck they meant by "anarchist".
That perspective points more towards perceived problems with anyone owning and controlling any large organization for any reason, doesn't it? It's basically 'power corrupts and the more power any single individual has, the more corrupted they become.'
Now, can you run large organizations with focused goals in what we'd call a democratic manner? Maybe a kind of multi-level (i.e. hierarchical) democracy, because why would you want someone with six months of experience having the same decision-making power as someone with six years of experience? Similarly, why would you want people not directly involved with the work (absentee owners and shareholders) making decisions about what kind of decisions the organization should make (i.e. which spaceship design is the best)?
It's entirely possible that humans have yet to invent the optimal organizational structure for coordinated efforts towards goals like establishing a viable human ecosystem on Mars, etc. Science fiction is of course an arena where such concepts can be speculated about, that's part of its value.