mpa applicant

Does anyone know if there are different acceptance rates for the different deadlines? The MPA programs I am applying to have early January deadlines for consideration for financial aid and then April deadlines for all applications. One of my letter writers is going into surgery and won't be able to write one for January - I can go to someone else, but I prefer her. I don't think I will qualify for financial aid, but if it will hurt my admission chances to apply in February rather than January, I would find someone else. Thoughts?