It'd be really useful if calculated metrics could be used for cohort analysis.When I try to drag a calculated metric into the field it remains grey, so I'm guessing this is something that's not currently supported.
Cohort analysis supports a set of inclusion and return metrics which group users in some way. What I see is even not all standard metrics are supported. So this may be due to design.
I couldn't find if this had actually been submitted as an idea, so I did so. If you're reading this thread, then it's probably worth the 10 seconds to click over and vote for it: Calculated Metrics in Cohort Tables in Analysis Workspace (I'm assuming the moderator will approve the idea fairly quickly).