Mathematically perhaps, but in real effect probably not.
Digital zoom is a poor tool.
It takes an image and zooms into it - often you feel it has simply moved the pixels apart.
So, if you are viewing your 4K camera on a 4K monitor, you will see the pixels move apart when you digitally zoom.
If you are viewing your 4K camera on a 1080p monitor, the digitally zoomed image may look pretty much the same on the 1080p monitor (you'll just be looking at a sub-section of the greater overall available scene covered by the camera).
An optical zoom allows you to zoom into the area of interest and clearly show just that zoomed area (at the available resolution e.g. 1080p in your example).
The result is clearer / much more obvious at greater zooms.
It is common for PTZ cameras to offer 24-36x optical zoom.
Seldom is more than 1080p necessary with these greater zoom ranges.
Because, when detail is required, you have the optics to simply zoom-in a bit more.