I'm a director at my firm and so have sat on a good number of hiring committees. This would be uncomfortable for me to read in the context of someone getting a job offer with another firm and turning it down so they could have a chance with us. It's too thirsty.

I do think it is very acceptable/encouraged to say you know you would look forward to accepting an offer of admission should one be made/it's your first choice/you felt motivated to apply to this school again/all of the above. There's a way to show genuine enthusiasm that can set you apart without being too extra or making someone feel guilty/uncomfortable if they have to waitlist/reject you.