I'm not sure how to answer this without pictures. I'll try.
Some compound bow sights have levels in them so you can ensure your bow isn't canted to one side or another. These sight levels can be especially useful for saddle hunters who may be contorted in such a manner as to imperfectly reference gravity, or the horizon, and be a bit off-kilter. So with regards to canting the bow side-to-side, you do want to level the bow. As a novice archer, you may want to install a pin sight with a spirit level like this:
However, obviously, we're shooting out of a tree at a target on the ground; we're shooting at a downward angle. In that sense, no, we absolutely do not want to have our arrow horizontal when shooting downward.
Your question also refers to proper form, but doesn't address it entirely. You'll want to read up on proper form, especially as relates to elevated shots. Briefly consider this archer:
His bow arm is perpendicular to the bow, his arms are (roughly) in line, and form a T with his upper spine. He's aiming downward with his whole torso, not just dropping his bow hand to aim lower. I'm not sure how far I've gotten away from your question about leveling the bow but I hope I've helped.