All of this is in your browser until such time as you hit the dropper. Ideally, you should have an add blocker like No-Script or Adblock to prevent the ads in the first place.
You can add the IP addresses given to the Norton firewall, but malware distributors move around a lot. Just blocking one or two sites will not protect you from redirects to other sites.
If you had been infected, it is likely that you would see lots of popups and ads on your computer.
I'm pretty sure I ran across this "in the wild" (was browsing on a known safe site, when Norton suddenly warned me it had blocked an instance of suspicious.cloud). So I'm pretty sure the answer is yes, Norton will take care of it for you.
And delphinium is right about the likely symptoms if something had gotten through.
If you'd like a second opinion, I'd recommend the free version only of Malwarebytes:
Different antivirus software has different strengths; this one is especially good at detecting malware on systems that have already been infected. Do not purchase or take the free trial of their full version, though: like Norton, it contains real-time scanners, and having two programs with those functions running at the same time will cause serious problems. The free version omits that functionality, so it's safe to use as a second line of defense.