The bill doesn't rely on DNS and moving the DNS system outside of the USA wouldn't stop COICA from working.

COICA works by forcing American ISPs to block their users' access to a list of domains. It mandates 2 lists; one where ISPs won't be punished for blocking and a second list where ISPs are forced to block. It's very close to implementing what China has with their Great Firewall. It's censorship plain and simple.