The schools will the pull the letters they need from your primary application, so no it won’t hurt you or anything. If for some reason they needed another letter and all of your LOR slots were taken, then you could use a letter delivering service. However, I’d just make sure you can satisfy all of the requirements for the schools you plan to apply to through your primary application to make life easier.
For example, I had a DO letter, MD letter, Committee LOR from my university, 1 non-science professor LOR. These four just about covered all the requirements for the schools I applied to at the time. Then I added 2 letters from different science departments at my university.
Is 6 still the max amount of LORs you can upload to your AACOMAS application?