To answer your question..... Yes, you can run 4k.
How fast will depend on the connection to the monitor.
It really does not take much to run a 4k monitor.
Intel integrated graphics will do it on a modern motherboard.
If you want 60hz, best to use a displayport connection.
At 30Hz, HDMI will do.
Read the specs on the motherboard if it is intel, it will tell you how fast each connection type can be.
AMD motherboards generally require a discrete card like the RX580.
But... if you are not gaming, then you really do not need such a strong card.