I haven't seen the text of the bill, so don't know for sure. If it says "resolvers must block site" then yes, running your own resolver would still work. If it says "domain registries must remove delegation" then it won't, but that could only be enforced for registries that are based in the US. Unless your ISP blocks well-known DNS ports, which none due as far as I've found.

The article says one of the requirements for the complaint needs to be that the site to be blocked must be found to be foreign based, so I guess the assumption is that the current set of laws to take down the site or sue are unavailable.

So is this an opening move with an end goal of “private national internets”? Fracturing the international nature of the ‘net seems like every power worldwide would like and benefit from this.