It should be fine. I wash almost anything that comes through my hands, if anything I notice the smell is stronger afterward (not being under dirt)
I use those (the erasers), little ivory bar soap, and a conditioner with the mildest fragrance I could find on all my ponies.
PP- adding conditioner to the hair, and combing from tips to roots with a wire cat slicker (got an inexpensive one just for my ponies) works great! You wouldn't believe the kinds of stuff I've found hidden in that kind of hair.