There's a little box at the top of the Duty Finder that allows you to join duties in progress, but I have some questions about how this option works.
Does this only queue you for duties in progress, or does it also dump you into brand new duties? In other words, is this a "get me the shortest queue possible" button?
Are there any bonus rewards for completing a duty that you joined partway through? If so, does the bonus differ between Raids, Trials, and Dungeons?
Best Answer
No, you are not restricted to just in-progress duties
Enabling the option of joining in-progress duties simply expands the available duties you could join. This translates into (potentially) reducing your queue time since a duty in progress that has a member drop is a potential duty for someone who has enabled this option. However, my experience has been that I'm still much more likely to join a fresh duty.
No, there are no bonus rewards
In fact, it could be argued that your "rewards" could be lessened from joining an in-progress duty. Since the existing group in the duty could have progressed enough to kill one or more bosses, joining a duty such as that which had a member drop out means that you've lost the opportunity of loot from any of those bosses that had been killed before you joined. So, if you're looking to kill specific bosses that are earlier in the duty instance for whatever reason, you may lose the opportunity to do so if you happen to join a duty that is already in-progress.
On the opposite side of the coin, joining an in-progress duty should mean that you spend less time in the duty itself since it is (ideally) partially completed. Occasionally, you could be dropped into an existing duty that is just about to confront the last boss. If you're simply looking to complete duties as quickly as possible, this would be the best-case scenario for you.