Unless his attorneys are going to go up against YouTube's attorneys and drag this through to the Supreme Court (that is, unless he has a few million dollars sitting around earmarked for his lawyer), it can and will be stopped by a cease and desist. If YouTube sued him, they'd probably get an injunction preventing him from distributing youtube-dl until the case was resolved.
Even if it were litigated all the way up to SCOTUS, there is no guarantee that the Supremes would see a video downloading device the same way they see a video recording device (and the ruling that stated home recording was fair use, Sony Corp. of America v. Universal City Studios, Inc (colloquially, the "Betamax case"), was itself a controversial 5-4 ruling) instead of the way they see a peer-to-peer distribution network like Napster.
There are many spurious C&Ds sent to people for violations of the CFAA based upon a site's Terms of Use each year; big companies squashing competitors they dislike, or even non-competitors that embarrass the company by providing a service that they've as yet been unable to figure out, etc. The argument that violation of the Terms of Use constitutes unauthorized access under the CFAA has prevailed in court multiple times, and even if it hadn't, once a C&D is received, the authorization is at that point certainly revoked and thus, continued access equates to a violation of the CFAA.
There are copyright and trademark issues here too, even if you can prevail on the CFAA issues (not likely). Judges have ruled that downloading a webpage into RAM in order to extract non-copyrightable data is copyright infringement, because the momentary existence of the entire page in RAM is an unauthorized copy.
Various counterarguments that shift the blame to the consumer, e.g., "we don't actually talk to YouTube's server, we just take a URL that the customer submits via the extension and convert it to another URL, and that doesn't involve accessing YouTube's servers", usually fail (though logically extension developers shouldn't be any more liable than browser developers for their customers' use). One could be considered a conspirator or an accessory to CFAA violations.
So, yes, it could and would be stopped by a C&D unless Richard Branson or some other megamillionaire is secretly bankrolling youtube-dl, and even then, its chances of surviving the legal battle unscathed are pretty slim.
Similar considerations apply to something like PriceZombie, which Amazon just shut down because it doesn't like what the data reveals. The legal situation here is a seriously understated social problem.
You may read this and say it sounds like web crawlers like Google are illegal. Well, yes, they are. The difference is that Google was able to hit critical mass before such a devastating lawsuit was brought, and now they're effectively too big to sue out of existence. If you are making an internet company or product, you have to hope this happens to you before you make someone mad and get sued to death.