If the application fee isn’t an issue, and you believe you can successfully complete your other application in time, definitely apply to Pomona. You never know what could happen in admissions!
As a current international student at Pomona, to clear some things up about Financial Aid, contrary to what @steenbee previously said, it is NOT need-blind for us. It is need-AWARE, but if you are admitted they will meet 100% demonstrated need. This is not the same as it being need-blind.
This being said, it’s true, that if you need a lot of aid and are international, you are going to have to be a pretty freakin amazing applicant. If Pomona is your dream, it’s time to get fired up about college admissions. Get to know your regional admissions officer, be innovative and different in your high school career, take on leadership opportunities if they present themselves! It will be difficult but nothing is impossible!