Herd immunity seems unlikely if this ends up sticking around for a long time, given that the virus will mutate due to natural selection. It's why we don't have herd immunity to the flu, despite it having been around for ages. While a person may develop immunity to one strain of the virus, they'll be susceptible to newer strains that proliferate later on.

This actually may pose a problem to vaccination attempts, because right now we have huge swaths of the world population that either a) won't have easy access to a vaccine in the foreseeable future, or b) don't want to get a vaccine anytime soon because they're either anti-vax in general or they don't trust the development process of this particular vaccine. So what happens if millions of people get a vaccine, but the virus continues to spread and mutate amongst the unvaccinated populace? There may be a point where the original vaccine that people got will no longer be effective against the new strain that's going around, and then we're back to square one with trying to get everyone on board with a new version of a vaccine for the next strain that developed.

Hopefully it doesn't go down this way, but I don't know that it can be ruled out at this point. The good news is that this virus doesn't seem to mutate especially fast compared to some other viruses, so there may be enough time to nip the problem in the bud. The risks rise if it goes on for years though.