It's very possible that movie may underperform at the box office, especially in the US; though I think it will do decent in the foreign markets.
There's no doubt the hardcore Godzilla fans will see it, but will the general audience?
Very likely yes they will see it, besides the general audience who has been around after the 1998 film, will be greatly curious in wanting to see if this Godzilla will be better than the 1998 film.
The leaks of the comic con trailer, the knowledge of the cast within this film, the dark atmosphere and tone, almost every scrap of news, and the official teaser trailer has drawn a very large interest from the general audience.
I've seen many non-Godzilla fans and people with little childhood experience with the icon wanting to see this film this year. And with Godzilla being a iconic franchise and monster, it's going to draw in more movie-goers.
The major question is, will this movie be marketed well enough to keep drawing in more people? Exposure is everything, too little and people won't know the film's existence and when they do, probably won't care enough to go see it. Too much exposure, and you might end up spoiling too much about the movie, or spend a little too much of your marketing budget.
If the 1998 film had one thing, it was huge marketing, and exposure of the icon was pretty massive due to channels running Godzilla marathons and airing movies as hype towards the film's release. If we can get some of that this year before the movie's release, I think things will be fine.