It can be viewed that way, insofar as your order, or sequence, is correct. Nevertheless, when questions are asked about how it all happens, it becomes obscure because of the terminology specific to the theory. In other words, if the logical sequence leads to a certain conclusion, the wording of the conclusion cannot be used beforehand. This means we don’t experience phenomena or representation because phenomena occur in a series of steps before representation and representation occurs just fewer steps before we can call it an experience. Between is understanding, judgement, cognition, knowledge, then finally, experience.
Thing is, nobody questions reason in common everyday living. When you sense a touch, you immediately experience what reason has only allowed as phenomenon whether you know what touched you or not. By the same token, you do know what touch entails because you have been touched before, so you have extant a priori experience of being touched, hence intuitions of things that can touch, even if you do not immediately know what touched you this time. This is of course, more commonly referred to as just plain ol’ memory.
Another problem with this kind of idealism is that much liberty is given to the enunciation of “faculty”. In one place Kant will call representation a faculty but in another he’ll lead one to think of it as an object of some other faculty. Intuitions are representations but reside in consciousness, which really cannot be a faculty of representation because there are notions and ideas also resident in consciousness which cannot have representation, re: infinity, space, time, and other supersensible conceptions, including those cursed noumena.
Kant also acknowledges the theory is quite incomprehensible to those who do not wish to understand it. But if it is understood, it should be found sensible, intelligible, indeed logically possible, but nonetheless no ways near apodectically certain. It is, after all, just a theory.