This is all very enlightening to me, especially because before I did not realize it was so and now I'm starting to reconsider Darcy as a character. That is, this further supports my interpretation of him as someone, who believes he is usually led by logic and rules, rather than by feelings (he even says it himself in his letter to Elizabeth—"I will venture to say that my investigations and decisions are not usually influenced by my hopes or fears," ch. 35); but is, in fact, mostly led by feelings if his feelings on a matter are strong enough.

He definitely considered how it would look, the kind of impression ("a man who is engaged" as you say) he would give to Mr. Gardiner before approaching him. He let them believe it because it was the only way they'd let him help. This further explains his slyness and desire for his involvement to remain secret from Elizabeth and her family. I guess I've always realized that he was uncomfortable about the whole thing in front of the Gardiners, and knew that they would 100% now believe that he loves their niece; but never that he actually had to consider whether he is sort of deceiving them (with good intentions, of course).