I am reconsidering the promotion/proposal combo link per your comments. I am not inclined to say Henry was acting or lying about the receipt of the letters. He was waiting “for very little more than opportunity” (30) and ‘very little more’ could suggest he was waiting for confirmation of the promotion before proposing. It does not seem to me Henry feared William’s promotion would not happen rather it seems he was impatient of the difficulties which prevented it being finished on his time-table:

I will not attempt to describe; how severely mortified, how cruelly disappointed, in not having it finished while I was in London! …But though my uncle entered into my wishes with all the warmth I could desire, and exerted himself immediately, there were difficulties from the absence of one friend, and the engagements of another, which at last I could no longer bear to stay the end of… I came away on Monday, trusting that many posts would not pass before I should be followed by such very letters as these. (31)

Henry called ‘at an earlier hour than common visiting warrants’ (31) because he received the letters confirming the promotion. It was luck that the first opportunity to be alone with Fanny presented at that moment but I have to ask why Henry could hardly bear anyone else share with Fanny the “first knowledge” (31) of William’s promotion:

Henry, overjoyed to have her go, bowed and watched her off, and without losing another moment, turned instantly to Fanny, and, taking out some letters, said, with a most animated look, “I must acknowledge myself infinitely obliged to any creature who gives me such an opportunity of seeing you alone: I have been wishing it more than you can have any idea. Knowing as I do what your feelings as a sister are, I could hardly have borne that any one in the house should share with you in the first knowledge of the news I now bring.” (31)

Is having Fanny alone to announce the promotion to benefit him in some measure or is it only to increase Fanny’s happiness? Could he think Fanny would be less happy to hear the news with other people in the room? I don’t think so—after thanking Henry the first thing she wishes to do is tell Sir Thomas. However Henry could expect the same benefit from being the bearer of such news as he did when he wanted to give her the first knowledge of the Antwerp’s return. I don’t think Henry would fail to consider the effect of announcing the promotion as a past similar announcement had some success:

He proved, however, to be too late. All those fine first feelings, of which he had hoped to be the exciter, were already given. But his intention, the kindness of his intention, was thankfully acknowledged: quite thankfully and warmly, for she was elevated beyond the common timidity of her mind by the flow of her love for William. (24)