Would Kant have accepted the argument from desire?

Probably not, since he almost certainly would have regarded the desire as an inclination.

From Kant's Critique of Practical Reason:


*(2) In the Deutsches Museum, February, 1787, there is a dissertation by a very subtle and clear-headed man, the late Wizenmann, whose early death is to be lamented, in which he disputes the right to argue from a want to the objective reality of its object, and illustrates the point by the example of a man in love, who having fooled himself into an idea of beauty, which is merely a chimera of his own brain, would fain conclude that such an object really exists somewhere. I quite agree with him in this, in all cases where the want is founded on inclination, which cannot necessarily postulate the existence of its object even for the man that is affected by it, much less can it contain a demand valid for everyone, and therefore it is merely a subjective ground of the wish. But in the present case we have a want of reason springing from an objective determining principle of the will, namely, the moral law, which necessarily binds every rational being, and therefore justifies him in assuming a priori in nature the conditions proper for it, and makes the latter inseparable from the complete practical use of reason It is a duty to realize the summum bonum to the utmost of our power, therefore it must be possible, consequently it is unavoidable for every rational being in the world to assume what is necessary for its objective possibility. The assumption is as necessary as the moral law, in connection with which alone it is valid. -