At this time it does seem like clicking edit is a work around, and will let you pass any audit in those two queues.
UPDATE : CONFIRMED Just robo-reviewing by clicking edit right away on the First Posts Review Queue will let you pass any audit it throws at you. I haven't been able to confirm this for Late Answers Review Queue, but I suspect it's the same.
First test : First posts review queue. Clicked Edit on a post that was an audit that's correct choice was No Action Needed , but I passed the audit.
Second test : Same as first test.
Third test : First posts review queue. Clicked Edit on a post that was an audit that's correct choice was any of the following: downvoting, editing, flagging, or closing.
How I suggest that it should work :
If a post should be No Action Needed, it should mean what it says, thus no action should take place by you, the reviewer of the post. Trying to edit the post should be considered attempting an action, so you should fail the audit for trying to edit a post the doesn't need any action. If people really want to edit the high quality post, they should just open the post in a new window and edit from there, instead of the review queue.
Likewise, if a post is bad, acceptable actions by you already seem to include, editing the post, downvoting, flagging, or closing. So any of those actions you attempt will be considered correct, and you will pass the audit. So no changes seem to be needed there.
Since there were no moderator comments or anything on this question, I posted a comment to a moderator on a some-what related thread here.
Side question as well: If someone could use this to perform the
workaround, shouldn't there be some sort of protection other than the
review limit? Or is it not much of an issue?
So to answer your side-question, it does seem that in general, there are already other protections in place. However, from what I can tell, there wasn't an automatic detection in place for this exact workaround. But there is a way to manually detect someone trying to use this workaround. So now that this workaround is well documented, I would think moderators will check for it every so often hopefully, to catch anyone trying to game the system in this manner. And at least as of now and in the past, this workaround didn't seem to be much of an issue.
Is there any type of audit, such as one that clicking flag is the
common sense action to pass, where clicking edit would not pass it?
As of this time, I highly doubt that. However, maybe it's possible that spam audit types would not accept clicking edit as a pass, but again, I doubt it.