Facebook is currently about '$1 profitable' per-profile. So yes, far-fetched.
You know that is irrelevant to their valuation. That's not how investors are valuing the business.
As far as valuations go, FB is valued the same as Amazon with respect to earnings, i.e. they both have the same P/E roughly (not that this metric means much, but it's a widely used one). Amazon is barely profitable as well, yet people feel it's a great investment - or greater than FB.
Swings and roundabouts.