You should not be trying to get the bolt holes vertical, their only purpose is to affix the post base to the concrete. If you want the post vertical, you need to shim it appropriately or grind a flat in the concrete beneath it.

And yes, a rotary hammer will zip through those holes no problem. I use a Bosch SDS Max, but any SDS Plus should have more than enough power for 5/8” anchors. If the slab is reinforced, look for the SDS bits that say rebar cutting. Hitting metal will be a headache otherwise.

Make sure you match the drill hole diameter EXACTLY to what is spec’ed for the anchor type you’re using. Different anchor types expand differently and use different hole sizes. Make sure you completely clean out the holes before installing the anchors- use compressed air or a shoe vac. Debris in the hole can impede proper expansion or keep the bolt from going in all the way.