It varies depending on location and time of day. Some of the locations are out of the way enough that you could walk in. Others, yeah, there's gonna be a line. I went to a few when I was around the areas, and based on my experience:
Kakigori. Kooriya Peace is right next to Inokashira Park, so it will have lines. But like on the show, you can reserve a spot, or if you don't plan to be around Kichijoji for long, there's a short wait to do take out. There's also Amaikko, where Kantaro tried to go but had a long line in the show, was actually less crowded.
Parfait. Kajitsuen Liber is fairly close to Shinjuku station. Chances are no matter when you go, there will be a quite a line. And the specific dessert from the show is seasonal.
Savarin. Recherche is in Yokohama and not near anything super busy. Small place but no wasn't crowded. Chances are the owner will ask if you went there because of Kantaro.
Eclair. Rue de Passy is a small patisserie, a little out of the way so doubt you'll run into crowds or lines or anything. Although, I didn't actually try an eclair there.
Chocolate. Minimal is close to yoyogi park, didn't seem crowded. I saw another location in Ginza. I think on the show they just had chocolate bars? You can just pick up a box or something. They did have other chocolate focused desserts if you wanted to eat in. When I went they had a chocolate parfait on the menu that was sold out, and this must've been around 4 or 5pm.
Mont Blanc. Waguriya is on yanaka ginza, which seems like a decently popular shopping street/shotengai. This will have a long line. Other than the parfait, this is the only one I waited in a line for. I have little patience for lines, but it was kinda worth it. Probably the best thing out of the ones I did try; I'm between it and the savarin.