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No, not irrelevant, unless "free" users also cost you nothing.

They don't have to cost you nothing, just little enough that you're net ahead. And since startups that use the freemium model invariably manage to make free accounts cheap, I assumed I didn't have to mention that explicitly.

But isn't the percentage of users who pay what determines whether you're net ahead, and not the total number of paying users [1]?

If Dropbox has ten million users paying them $10 / month, but they have to support another billion free users for twenty cents per month each, they're screwed.

1. Assuming you're making enough to cover fixed expenses

Not in practice. Usually startups arrange that the incremental cost of one additional free user decreases as the number of free users increase.

profit = paying users * price per user - total users * expense per user - overhead expenses

Business on the internet seems to be much more about driving up total users while driving down expense per user, rather than driving up paying users / total users.

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