Based on my experience, you get more accurate. I am currently at archery skill 8 now, and frequently 1-shot lesser zombies and predators at close range, because the increased accuracy also translates into more ‘good’, ‘critical’ and ‘head-shots’.
You can now craft your own mods for bows, which improves accuracy by decreasing dispersion. The result is that you have to aim for a few seconds to achieve maximum steadiness, which will improve your accuracy/quality of your shot. After aiming, you can keep firing arrows at maximum steadiness as long as you don’t move, even if you change targets, because bow/arrow has zero recoil. This can take out entire hordes of low ranking zombies (may consider footwear with acid protection for those pesky spitters if you want to stand and deliver legolas-style).
Drawspeed is unaffected by strength/skill as far as I know.