Unless it's an exact match (eg. non-profit.company) to their current name, an established organization would probably see it only as an additional non-essential cost. But an emerging, youthful organization wanting to reach an evolving, newer audience, a matching ngTLD might definitely garner their interest.
Although most projects or non-profits are assumed and identify well historically with .org, there's no reason why credibility couldn't be created with the actual work the organization does, and with an ngTLD that perfectly matches their name.