Yes, but I'm sure this will only be valid for big enough companies (read serving millions of EU citizens) as it's subjective what "processing the data of EU citizens" actually means. It's not realistic to expect every minor mom&pop eshop or minor online service worldwide to appoint a representative in the EU. Furthermore, enforcing these rules will highly depend on international relations as it's outside of EU jurisdiction and it can only reach non-EU companies by collaboration and signing treaties with other governments, so this means USA and maybe Canada, but I highly doubt to see companies from China or Russia etc. to be held accountable.
Well, only time will tell, I just relayed what I've heard from people much more knowledgeable in this area than me. How I understand this is that if you serve many enough EU citizens, please be kind, open a branch in EU or at least send a representative, because you are de-facto doing business here. Mainly this is to avoid situations where, for example Facebook, closes its EU offices and pretend to have no EU presence (and no need to abide EU regulations) despite hundreds of millions EU citizens use their services.
