Definitely. An idea I've had in one of my notebooks, which I've never had the time to explore, has been based on mortals as food.That's three very different answers: food, pets/workers, and offspring would result in very different relationships between mortals and gods.
But any one of those would be interesting, and definitely a lot better than what FR (or most other official settings) give us, so I highly encourage you to explore whichever seems interesting to you. Your game will almost inevitably be better for it.
Basically, there's a cyclical occurrence (5-10k years?) where the gods help and encourage mortal civilizations to flourish. Then they devour the mortals for power and pleasure, and repeat the cycle. The higher echelons of the priesthood are in on it and are spared, in return for aiding the process (hiding the evidence, restarting civilization, hindering access to the planes so that people cannot easily escape, etc).
The campaign would start very vanilla, but over time the PCs would find increasing evidence not only of this cycle, but that it is about to repeat itself. Then it would be up to them to either try to find a way to avert this cataclysm, or at least find a way to abandon ship and escape. It's a touch derivative of Mass Effect, I admit, but I think if I pushed it towards a cosmic horror angle (the gods who love and care for you are actually monstrosities to whom you are nothing more than well maintained cattle) there could be something of promise in it.