No, not if you are using any economically sensible definition of cost (and thus of "free").

"I have to directly pay x units of currency" is not a useful measure of cost. There are lots of ways in which either you can be paying costs indirectly, or in which other people are forced to pay costs caused by you, neither of which really makes much sense to call "free".

Network effects are what economists call an externality: A cost (or a benefit in the case of positive externalities) that is paid for by people who didn't participate in the decision that led to that cost. Also, monopolistic structures and concentrations of power often have long-term consequences that lead to what economists call opportunity costs: A monopoly that hinders innovation, for example, might end up preventing a beneficial technological development, or even just lower prices due to competition.

That people often confuse "immediate payment" with "costs" is exactly the misconception that companies like facebook like to use to hide the costs.