To avoid confusion you might want to not call your vertex shader a geometry shader since the geometry shader stage is its own thing introduced with DX10.
The depth value is relative to the camera's position and as such corresponds to the world position "depth" units along the camera's forward vector.
Your posted code is incomplete, what type is OUT.pos and OUT.depth? I'm assuming a float4, in which case you will indeed write to the alpha component of OUT.depth, however... it will correspond to the w component of the position, whereas the depth in view space is stored in the z component.
Also it seems the depth is in screen (projection) space rather than view space since you multiply it by matWVP.
In this case you will need to transform it back into world space by using the inverse view projection matrix. That will only give you the Z coordinate however.
The easiest way to do what you're after is probably to store the Z coordinate in view space; this will be the depth relative to the camera.
Then you transform it into world space like so:
float3 wPos = CameraPosition + CameraForward * depth;
Disclaimer: I was quite tired writing this so I may have overlooked something, just thought I'd share my thoughts though.
"Why do programmers get Halloween and Christmas mixed up?" Because Oct(31) = Dec(25)