I am thinking for using Blackmagic Design DVI extender for video monitoring with FCPX.
FCPX has option for full screen monitoring on second computer display, and DVI extender
convert DVI signal to SDI. Is it ok to use it for non critical monitoring.
This should work just fine. You would just want to set the output resolution of the second port to whichever video standard you are using. (example 1080i or 720p). Basically you want it set to a video resolution and not a computer resolution.
Outside of that just make sure the DVI Extender is set in Video mode and you're off to the races.