Selecting no action only does that, take none of the possible actions. This will/should leave the file in place, but what it won't let you do is run it. After a reboot if you tried to run it again you would get the alert again.
OK, thanks for the clarification, but it actually quarantined it rather than leave it in place.
For many years avast has taken the decision not to have a single click option to ignore/exclude/allow to run for obvious reasons. If it was a good detection, then a single click (accidental or otherwise) could have serious consequences, for the user who might just blame avast for it.
I can understand the reasoning behind the policy, sort of, but it is disconcerting to think that the end user can't be trusted by Avast! to make decisions about what runs or what goes to quarantine. If it had been an essential systems driver instead of a third party application program I'd probably be typing this on my Ubuntu laptop now. In my experience most 'malware' flagged by anti-malware or AV's are false positives. I know they are inevitable in any AV program but there needs to be some safeguards. In Panda Free 2015 there was a choice to uncheck the default auto-quarantining of possible malware. This ability saved millions, including myself, from a severely borked computer during the recent great Panda borking event caused by a bad update signature. The ultimate irony here is that I changed my Win 7 desktop to Avast!, as I had had good experiences with it before on my Vista laptop, and because Panda Free 2016 did exactly the same thing with FotoSketcher a few weeks ago on the Win 7 machine! It was a false positive then as well. I thought I would have more control with Avast! Free.
I don't know if the DeepScreen popup is specifically branded as such. But if I recall it does say it is running a DeepScreen check and it may take a few seconds.
I've seen DeepScreen pop-ups and it definitely wasn't one of those.