Would it be in any way possible to bake cookies using a blowtorch?

In other culinary applications, blowtorches are used to put a sear on foods that you exactly do not want to cook at the temperature used for searing. For a demonstration, point a blowtorch at any kind of dough that you know would steam leaven if brought to a bulk temperature over a 100°C - the surface will be very visibly burnt quickly long before any steam leavening will happen. Also, you could handle the dough with unprotected hands seconds after applying the blowtorch heat - not advisable with dough that has been heated through in an oven...

Anything containing a lot of sugar will easily burn to a black char if brought to a temperature much above 160°C, as can be seen even with an oven: Bread or pizza doughs, being low sugar low fat, can be cooked in a 250°C oven - however, for pastry rich in sugar and fat, even 180°C means you need to keep a close eye on the oven in order not to get the surface of your baked goods burnt and bitter. Fat also matters because many fats and/or their impurities will also start to chemically change for the worse in that temperature zone, as can be seen with unclarified butter. Using a blowtorch would mean that you would thoroughly encounter all these negative effects on the surface before getting any significant heat into the mass of your dough.

While pointing a blow torch at cookie dough is 'possible' the direct heat is likely to caramelize the sugars too fast to get anything that resembles a cookie. If you look at The Science of Cooking they do offer some ideas but none of them would be consistent with the idea of baking a cookie.

There are a variety of articles and videos online about cooking other things with a blow torch.