According to my experience, some combinations of disc-pad materials do, and some don't. (Or maybe rotor/pad contamination does allow it to occur)
In some cases, the heat can cause a "glaze-on" coating to develop in the active surface of the pad, and this glazing has lower friction coefficient, low enough to be unable to lock up the front wheel while pushing the bike.
I once saw this happen to a another person's bike on a on a long, steep MTB descent (XC leisure ride). The rider asked for help about the brakes because more force than usual was required at the lever, stating that the brakes where "normal" before the descent. We cautiously checked the brakes, which by the time where not hot enough to cause skin burns. and where able to somewhat restore performance, removing the glaze with a bit of sandpaper (I carry sand paper as part of my patch kit). No thing was done to the disks at this time.
Other riders of similar skill level who descended at similar pace did not experience the issue, also, those other brakes felt cooler to the touch, although many of them had higher spec brakes. My guess is that the overheating/glazing happened either due to the pad state/material or due to contamination.
I've also experienced quick glazing on rim brakes (single pivot caliper brakes) on an old road bike. The dried up brake pads had little stopping power but felt OK while riding on flat terrain. I had scrubbed the pads and rims surfaces recently, something I regularly do on V-Brakes, but this time, during a steep descent I felt diminishing braking power until I could not use "burst brake" technique. Due to continuous braking, rims got hot enough to pop the tubes near the valve (I think new tubes could have withstand the heat). Luckily, I did not lose control. After the fact inspection showed the pads heavily glazed and rims smeared with black residue. This was somewhat an extreme case where many things combined to that outcome, but definitively, fresh, good condition pads should not have caused the issue to begin with. Old rubber pads seem to be more prone to develop a similar "glazing" than new ones. (Same bike performed OK once pads, tubes and tires where replaced)
Bottom line: Keep your brakes (pads and rotors) clean, as oil or other contaminants can also enable glazing to occur, even though in less demanding working conditions they may seem OK. Perform thorough inspection regularly and do not let pads get too old (I think this applies for both disc and rim brake pads).