No, reader Colin, no more than an ice cream will, and there are several reasons for that. Firstly because chocolate mousse contains lots of different dairy and cocoa fats, which, while they’ll firm, won’t go entirely solid. But additionally, mousse follows freezing rules that are similar to ice cream.
Consider some of the other key components of a mousse: water and sugar. Mixed together they form a syrup, and syrup does some very interesting things as it gets cold. At the freezing point, some of its water does indeed go crystalline (freeze). But as we know from other discussions on the topic of crystals, they only form with other like molecules. And that means that as some water molecules freeze out of the syrup, the sugar molecules get left behind in the solution.
Fine and dandy. However now, the syrup that remains has a higher concentration of sugar, which means its freezing point is lower. No problem, home freezers go down to zero Fahrenheit, so the syrup will get colder and more water will freeze out of the solution. But then that creates an even more intensely concentrated syrup with an even lower freezing point, and so on. This game goes on and on until the syrup’s freezing point drops below the freezer’s ability to freeze it.
So you see, no matter how cold an ice cream, sorbet or mousse gets, it will always contain some small amount of (very sweet) liquid syrup. And that syrup will make the concoction scoop-able, at least to some extent. Ah science, will you ever run out of wonders?