It doesn't happen too often - but I've had that happen several times, actually. Just like people might pretty much hire you (or invite you to substantially greenlighted interview process - sans whiteboarding or over-the-phone grilling) solely on the basis of a talk you gave, or an impromptu discussion about some topic you're insanely interested in, after meeting you at some event.

Granted, this has been for gigs (or temp-to-perm) situations, not official, up-front fulltime roles. And some of these people ended up being flakey or sketchy (as spontaneous / whimsical people sometimes are). But nonetheless, hired (or substantially fast-tracked into their process, bypassing most of the usual interview crap) - pretty much on the basis of single demo or code sample (or in one case, literally on the basis of a single stats plot).

Because by this point, pretty much everyone knows how silly those live fizzbuzz sesions are anyway - including those administering them.