Was Kant implicitly using UDT?

Consider Kant's categorical imperative. It says, roughly, that you should act such that you could will your action as a universal law without undermining the intent of the action. For example, suppose you want to obtain a loan for a new car and never pay it back - you want to break a promise. In a world where everyone broke promises, the social practice of promise keeping wouldn't exist and thus neither would the practice of giving out loans. So you would undermine your own ends and thus, according to the categorical imperative, you shouldn't get a loan without the intent to pay it back.

Another way to put Kant's position would be that you should choose such that you are choosing for all other rational agents. What does UDT tell you to do? It says (among other things) that you should choose such that you are choosing for every agent running the same decision algorithm as yourself. It wouldn't be a stretch to call UDT agents rational. So Kant thinks we should be using UDT! Of course, Kant can't draw the conclusions he wants to draw because no human is actually using UDT. But that doesn't change the decision algorithm Kant is endorsing.

Except... Kant isn't a consequentialist. If the categorical imperative demands something, it demands it no matter the circumstances. Kant famously argued that lying is wrong, period. Even if the fate of the world depends on it.

So Kant isn't really endorsing UDT, but I thought the surface similarity was pretty funny.