Simulating 1080p pan shot by cropping stationary 4K fisheye footage?
Yes, you can do this successfully. I did it with an overhead 4K action camera with a fixed fisheye lens (YouTube video here).

You'll want to remove the distortion in software to "square it up". Then you have some room to zoom in and pan. However, you effectively lose some resolution with the lens correction. You can only zoom in so far before it's noticeable.  Obviously it's not as crisp as nice 1080 video, but it may be perfectly fine depending on your requirements.