The description states that it 'removes recovery penalties'. Does this mean a master chain wearer will recover exactly the same as master leather, or are there inherent differences in the two that are not taken into account with that description?

Is there a way for me to see what my current 'recovery penalty' for my armor is?

In theory, yes, master leather and master chain will both give no penalty to your recovery time. In practice, it's bugged. GreyFace's patch (which does allow you to see recovery time) also fixes the armor recovery bug, mind.