Any downsides to upside down shelves?
Normally the long metal arm holds all the weight.  The screws are just holding the shelf in place.

With the upside down shelves all the weight is on the screws/bolts.  They will not be able to hold as much weight.  It might be good enough.  Or it might not and piles of books come crashing down on someone's head.  

There are calculators online to figure out how much weight a particular size piece of wood can safely hold with supports at a given distance.  I would see if you can make the shelf strong enough with supports on either side of the doorway.