>>2453064Answer: no
Mountaineering boots only have two advantages: they are rigid and they are warm (if insulated).
As for trail-running shoes, plenty of them are waterproof and some even have integrated gaiters. I recently did the Mont Blanc with a pair of Salomon XA Alpine 2 (crampons were Grivel Air Tech). They have the aforementioned disadvantages, but honestly unless the route you're taking is extremely technical this won't matter.