Will IMac my Radeon Pro 575 4GB card support the requirements for Final Cut Pro?

Any mac that can run the current OS can run the current version of FCP.

Your iMac seems to be a 2017 model, and so it can perfectly well run Big Sur and FCP.

If you are running an older OS, first make a full backup - never do a major upgrade without a backup.

Download the free trial and see for yourself how it works.

Also, if you are unfamiliar with FCP, I recommend you take some time to follow along the excellent introductory course at izzyvideo. It's free, too.

https://www.apple.com/final-cut-pro/trial/