Yes. The first bit of a sigmoid growth function looks a lot like an exponential growth function. In the real world, when you have exponential growth in anything, you eventually get a sigmoid if you're lucky and a crash if not.
"'Tis true, 'tis pity, and pity 'tis 'tis true." -- Poloniouius, in Willie the Shake's _Hamlet, Prince of Darkness_