Should I paint wood in a roof that is not directly exposed to the outside?
You can seal the wood after it is framed.  Do you need to?  No.  Would the framing last longer?  Probably.  Does it make sense to do this?  


if you like to spend a little extra money on frivolous things...
if you feel like that there is no one monitoring the house during parts of the year.  Obviously it had access to moisture because it was a balcony.  So maybe a monsoon could hit the room hard and no one is checking on the house for a few months.  Maybe this helps the framing last longer after decades of use and many unmonitored monsoons.  
if this is an indoor/outdoor room