The only two chains I've broken (as in a link sideplate has snapped, clearly under the influence of my AWSUM POWR) have been on fixed, though I once popped a joining pin out, back before I discovered quick links.
In one case, lack of a chain tool was mitigated by being 300 yards from Decathlon, though that resulted in me owning an extra chain tool I wouldn't otherwise have needed.
Even with a quick link, you'll need a chain tool to push out a pin and allow you to fit it, unless you plan to get both creative and lucky with your choice of tools improvised from roadside debris.