Hm... I think it would be kind of a stretch, based on what I've learned about the elements that typically come up in Gothic fiction. There are examples of Gothic architecture discussed in the Brick, but I don't think they're really a centerpiece of the story like they are in Gothic novels. Cosette fulfills the "virginal, pure, innocent female character" role, and I guess we could say Valjean fulfills the hero's role in rescuing her from the Thénardiers (who in this case are a combination of the "villain" and "bandit" archetypes if we look at it as a Gothic work). Marius also works as a "hero" character, but doesn't actually save the "maiden" from any villainous figures.
But there isn't really a central villain character the way there typically is in Gothic works, either -- Javert is the main antagonist for Valjean but not actually a villain, and Thénardier doesn't really control the plot the way the villains in Gothic works tend to. If there is an overarching villain in the story, we could argue that it's the State and its system of oppression against the poor; but having such an abstract and nebulous "villain" isn't really something typical for the genre. And whereas Gothic works tend to portray the clergy as weak, corrupt, or villainous, Les Misérables
tends toward very good and generous Church figures -- especially the Bishop.
It's an interesting idea, but I think the Brick only has a few passing similarities with Gothic novels. I'd be interested to see what others think, though.