Well, again, almost. The nature of a fisheye is the distortion is more apparent farther away from the image center.
Here's a 16mm Nikkor fisheye shot and the same shot with the 1.5 crop. If you backed up far enough to cover the same amount of the foreground subject, this area would be coming out of a less distorted area of the image projected onto the imaging plane.
So while an effective 24mm non-retilinear lens is heavily distorted, it's not a fisheye anymore.
With a true circular 180 degree angle of view fisheye, the crop would lop the top and bottom off the image circle for a shot made with the camera held horizontally.
To visualize why a crop is less distorted, imagine a camera with a 20X crop factor. When you trim away the extreme distortion of the outside of a fisheye image, the center is only modestly distorted since the fisheye distortion is a spherical projection.
Of course if you want a fisheye effect you can use the spherize effect in Photoshop to create one. Just be sure to make your canvas square if you don't want an eliptical distortion...