If it will tell on the application process then simply refuse it. At this stage I guess what is important to you is entering a Medical School.
I am a physician who recently has taken time off to do more research. And trust me I want somebody to abuse me...when it comes to grant writing. Knowing how do it is very important and it isnt something you just wake up and start writing...u have to try a lot of times to master it. Ofcos in years to come....I wouldnt be interested and would have some juniors write it.
If u have no experience then looks the professor is actually setting u up to learn. I think it is something which could enrich you. However a big no...if it will affect your Med school aspirations