Letters of Continued Interest

Hi all!
I’ve gotten into Yale and Oxford but I got waitlisted at UChicago. However, I am very intrigued by the school and I would really like to have UChicago as an option. Would it be appropriate to send a letter of continued interest even if I am not sure I would go there even if I got in?
All advice appreciated.

What does your getting into Yale and Oxford have to do with anything?

I thought it might be useful context for the situation to know the other options I am comparing UChicago with.

And or to brag…

Yes, you can send a letter of continued interest.

No, that was not my intention nor did that cross my mind. Simply sharing information about where one has been accepted does not constitute bragging.
OK, so it is fair to send a letter regardless of whether I am committed to attending the institution…?