I’m actually running FCP X on an few unsupported graphics cards.
First is a MacBook Pro 3,1 (2007) NVIDIA GeForce 8600M GT. It is open CL, just not enough vram. FCP X runs just dandy if I am dealing with SD, or Proxy for HD projects.
Second is a MacPro 2006 1,1 with a NVIDIA GeForce 7300 GT. This one I get a warning that the graphics card is unsupported. It barely works. Very sluggish. Much slower than the lower clock speed MacBook Pro. However, I have a Radeon 5770 in the exact same MacPro in another office and it works like very well with FCP X. Handles 1080p, 2K and even 4K just fine.
I would go ahead and try the trial of FCP X on your box, but in reality you need more Ram and I would get a new video card too. The 5770 should work for you. I would buy as much ram as you can afford. 12GB being the minimum I would use.
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T. Payton
OneCreative, Albuquerque