Yes. Especially if the cookie is still in its dough state. Every baker has struggled with custom designs with little bitty appendages that snap off when you are attempting to move it from the frozen tray to the baking stone (I'm looking at you little aggravating pom pom on top of Santa Claus' hat!)
If you ever break a cookie (and if you bake, you will), you can rescue it. All you have to do is put it on the stone and touch the broken parts together. The heat in the oven will actually fuse the cookie together. You may see a little line where the break was but if it is going to have frosting on top of it, nobody but you will know. Fixing a cookie is an easy procedure, and even if you can't fix it, you can throw the whole thing back in the bowl and you still haven't lost anything. Breakage happens more often with custom cookie cutters than with standard cutters. A star, heart and flower are nice big, sturdy cookies. But you try to make a scrawny snowflake, or Olaf's little twiggy arms or the tassel on the mortar board or the antennae of a caterpillar and you are going to break some. First, the dough wants to get stuck in the smallest areas of the custom cutter. If you run into that, here is your solution. Don't press all the way through the dough in the tight spots (any place you can't fit your finger through). Get the cookies hard frozen then whip around the edge with a little paring knife. It will save you a lot of ugly words. I find that fusing the pom pom to the side of Santa's face will make the whole cookie more sturdy in the long run.
Here is another cool thing you can do with fusing. Anybody know a fan of these colorful building bricks? Cut your bricks with a rectangle cutter and your pegs with the large end of a frosting tip. Position them on top of the rectangle and then bake. The heat will fuse them together like it was one cookie to start with. How cool is that?
When you frost these bricks you will want to thin down your frosting and spoon it over the pegs so it will drip through the segments of a cooling rack. Trying to apply thicker frosting between all those pegs will cause it to puddle up and lose the definition of the pegs.
If you are trying to make a 34 for a birthday or anniversary and you only have a 3 and a 4 cookie cutter, touch them on the stone and they will fuse together. I don't usually try to fuse too many numbers or letters together because then it will make a cookie that is too big for one person. You can spell out Happy Birthday Ellie and bake them individually and frost them. Arrange them on the table and your happy message will feed 18 people instead of three.
If you have successfully fused cookie dough, post a photo in the comments for all your baker girlfriends.