That may not be an expense the rescue you are fostering for can afford but if you're able to donate the money, I don't see why not. You might ask your contact person at the rescue beforehand but, if the groomer is a good, patient groomer and you're paying, they'll probably be ok with it.
One side note, how old is the puppy? When was his last vaccination? If he is under 18 weeks, you should ask the groomer to disinfect the table and tools, wear fresh clothing and wash their hands. You should carry the puppy into the groomer so he does not touch the floor (and in any area that has been previously visited by lots and/or potentially ill or under-vaccinated dogs like dog parks, vet offices, high traffic dog walking areas, humane societies, etc.)
#FosteringaPet