Can a command waive a non-deployable medboard (anxiety, depression) due to lack of personnel for a deployment or rotation?

If you're deemed medically non deployable and given a non-deployable profile, you're not going anywhere. The Commander would have to jump thru so many hoops to get a waiver for that...it would be easier to just remove you from the roster. This is why they call Doctors.....Doctors.

Can they? In the right circumstances, yes.

Will they? Short of WWIII, no. And even then, probably not.

If you referring to the post Med Board determination as non deployable then no they cannot deploy you. However we often see many Service members discuss deployability without fully understanding what type of deployment, training, etc. if it is a rotation and or a training event you can be assigned as rear detachment of forward Ops support personnel. If you have been found unfit for military service and recommended for separation, again they cannot take you along regardless of the type deployment etc.

Having said that there are often commanders and or senior NCOs who sometimes believe they can get Service members to do things outside the confines of policy or regulation and get caught doing so, skmetimes not.

Make sure your understanding of deployment with orders, or sone other function for leaving your current assignment and the status of your separation. It is not complex you just need to read and speak with your Command and Jag. I have seen junior NCOs and above threaten a Soldier with deployment and the command is t even aware. So speak to your COC first, a minimum of Company lever, then the CSM of necessary.