Yes it will, especially if it's a good flat HA finish. Glossier finishes won't keep paint as well, but even high gloss HA will take paint. In a low abrasion environment, the paint job could last years, but will come off much faster than the HA coating.
If you want to use basic spray paint over top of the HA, i.e. want a different color or customized look: remove batteries before prepping & painting; wear nitrile gloves & clean the surfaces to be painted with denatured alcohol & a lint free cloth. If a good flat finish (zero noticeable sheen in a well lit room when dry) use 1 or 2 very light coats of primer, followed by 2 to 3 light coats of paint. If the HA has noticeable sheen to it, use up to 4 very light coats of primer before applying finish. The glossier the finish, the more primer is going to help retain the paint on the flashlight.
If you want a better than HA finish though, you need to use Cerakote, sandblast the HA coating off, & follow very closely the procedures Cerakote has outlined for applying their finish, especially the prep & curing stages. When done correctly, Cerakote (oven cured variety) is currently the most durable finish on the market and is roughly 2 to 4 times more durable than the best Mil-Spec HA type III finish.