I don't know of anyone who has a perfectly hair-free face from laser. I suppose if someone has a sparse jet-black beard and transparent Nordic skin they might get that level of results, but for normal people expect a reduction in hair, but not eradication. If you want proof of this, try to tell the laser place "I'll pay you $3000 if I can keep coming in until I have a smooth face." They won't go for it because they know, as they say in the business "Results Not Typical."
That means that you're going to need electrolysis no matter what, and that isn't exactly fast. Even if you opt for the "pluck-o-thon" approach you're going to have to go through several sessions and quite a lot of clean-up over several months.
I speak from experience. Seven laser treatments and six month of two-hours-per-week electrolysis. I am making progress but hair-free is still a ways away.
