To answer my own question, some lay research shows it seems it is technically possible for them not to merge if only a tiny portion of their apparent event horizons merge and for only very briefly.
But this is because of a distinction between the Apparent Horizon [1] (which is coordinate-dependent) and the true global event horizon. So they appear to briefly merge but no true global event horizon forms to encompass both. I think!
Would they still fully merge, or might you get a mass exchange between them? Or even a smaller black hole spun off?