Yes, to a degree. The distance helps perspective, but the cropping can remove many pixels of image size.

The key for portrait perspective is to stand back a bit. The camera standing back at least about six feet, and 8 or 10 feet is considered better in the formal studios. What focal length this could use for a desired field of view would depend on the camera sensor size. Use the focal length that gives the desired view when standing back, but it is the distance that fixes perspective (enlarged noses, etc).

We guys may not ever notice the problem, and the ladies may not realize exactly why they don't like the picture, but they will like those standing back a bit better. It's more like their idea of their picture.

For the 35 mm film format, the 105 mm lens was considered classically good for head and shoulders portraits, because the focal length required standing back at a good distance to see the view.

But not all portraits are head and shoulder, some are chest and up, or waist and up, or some might be even full length standing portraits, or even group shots. It is OK to use a shorter lens for the wider view, as needed, but standing back at least about six feet is still important. I prefer 8 or 10 feet, which is necessarily a longer lens.

You didn't mention sensor size, but most cameras today use a smaller sensor with shorter focal lengths to still get the same view. That's fine too, but standing back at least about six feet is still important. The right lens is the one that gives the desired view from the proper distance.

Standing back and zooming in as desired for the view is fine, no problem. It can still be just a head shot if desired, but the key is standing back a bit.

Standing back and then cropping for the field of view you want will help the perspective, but cropping costs many pixels, the image may not print as large then as you would like.