Experimented with this some hours yesterday.
When approaching people with a dagger, people usually use holds or feints to make chambering as hard as possible. With the quickdraw however, you can switch to the dagger immediately and it is ready to strike withing a few milliseconds. This allows for quite a neat combo for me as an archer:
Run at people with bow ready. People will think "OMG stooped archer ! Archer cant block with bow". People will just swing without using holds or feints and then POW, I use the quickdraw and chamber the swing a few milliseconds later. Thats how fast it is.
There is a "cooldown" however while drawing a bow and some short period after so you cant instaswitch after just releasing an arrow. It also doesnt seem to work when you are hit. I am further investigating this, possibly you can chain it with some neat nudges.