I don't think he should keep his place, especially because long term I still think he'll make a better centre back.
That said I think it's really interesting that Martinez played Baines in centre mid in the friendly he organized against Porto. Seems to me he must seriously be considering using Baines as a midfielder long-term.
I know it's simplistic to look at what one player has done (Lahm) and assume that another could therefore do it (Baines). But on paper they're pretty similar players, and Lahm has a done a great job for Munich.
Given that Barry will need to be phased out at some point in the (hopefully near) future, would Baines be such a bad option? His pace and distribution would certainly be an asset - I guess it just depends whether he can get used to the positional discipline you need for that role. Quite excited to see if it works though.