Upvote:2
According to the first Google hit http://www.chamonix.net/english/mountaineering/climb-mont-blanc , the route you describe is the "Cosmique Route", and it says ****The ideal period is from March to September (depending on conditions)**. So the answer to the question is yes.
However this route is also much more technical than the standard route (see the text), so besides endurance you also need good technique on steep glaciers and with ice axes, you need alpine experience.