Yes, they'll almost certainly get enough signatures to make the ballot. Oregon's referendum process is designed to set a fairly low bar for that step. But its chance of passage in November is quite low. The measure isn't well written, resulting in a high probability of unexpected legal consequences if it survived judicial review. Because of that, advertising campaigns against it (which would be very well funded) will highlight those unexpected consequences in a way that can produce little effective refutation.

Comparatively liberal as Oregon is, it's still a western state. Large numbers of "blue" voters are also fishing and hunting enthusiasts.