Swamp ash really does have a very open grain. Even if you dont want to fill so its smooth and be able to keep texture you might need to still seal it in some way as any finish could be absorbed more than expected. Especially with end grain.
If you have an offcut of the same piece of wood, which probably isnt the case if you have bought the body, the ideal would be to test on the offcuts. An alternate might be to do some testing in a less visible part of the body, neckplate area for example.