If he is consistent on this question, then yes, I believe he must. Setting aside whether he really is consistent, let's consider one of his most famous statements on the matter, in A Treatise of Human Nature (quoted here):
’Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. ‘Tis not contrary to reason for me to chuse my total ruin, to prevent the least uneasiness of an Indian or person wholly unknown to me. ‘Tis as little contrary to reason to prefer even my own acknowledg’d lesser good to my greater, and have a more ardent affection for the former than for the latter.
The first sentence is the most famous, but for our purposes, the last sentence is the most important. As I read it, it says that there is no rational cause to prefer a better outcome to a worse one, even if you rationally believe that the better is the better, and the worse is the worse.
This lines up pretty neatly with your proposed syllogism. Say you want X, but you prefer not to do Y. Say even that you desperately want X, and every life outcome that is possible for you would be better if X, and you fully know it. Here Hume directly says it is not contrary to reason to prefer not to do Y, in spite of all that.
Now the only thing that clearly differs (to me) between Hume's statement here, and your four statements, is that in the fourth statement you say that you "ought" to do Y, given 1, 2, and 3. So the main question is whether there is a clear difference in this situation between what you "ought" to do, and what you "prefer" to do. And I don't think there is, at least not necessarily, as a syllogism would require. In a very, very large number of cases, what you ought to do is just what you prefer to do.
To make this concrete, suppose you strongly prefer to sleep on your side instead of your back. It seems obvious that you ought to sleep in your side in that case. Now suppose you learn that sleeping on your back will extend your life expectancy. And suppose you really want that! Nonetheless, if wanting that doesn't change your fundamental preference for sleeping on your side, then it seems uncontroversially true that you ought to continue sleeping on your side.