Can you use red pex for cold water and will it pass inspection?

Assuming you are talking about domestic use the answer is yes. Many installations use blue for cold and red for hot but that is to keep any possible confusion or accidental cross connections. Color does not alter the pipes rating or use. Check with your local building department to insure they do not have some local regs about color.

I agree with ballengerb1. Red is rated the same as blue and white. Same pipe, just different colors. I know of no codes that mandate red strictly for hot. You could run the complete system in red, or blue, or white if you wish. However, as ball mentioned, check with your local inspector to see what they have to say.