Ash would probably be too cool against a dark brown. A warmer purple might be nice. Avocado would probably be a better choice than shamrock, too. Maybe even moss depending on how dark your brown is.
Purple would probably fade to a grey anyway so might be a cool choice?
Ash grey might be very difficult to achieve if you have already dyed hair/ it will take multiple sessions. Also bear in mind green might stain your hair so you might have limited colour options afterwards (but i guess its just tips so it doesnt matter)