I don't see why you couldn't send paid FB traffic back to your site, as long as your following the Adsense TOS. Then again I'm not Google.

Not sure how you can justify a profit when you only know the cost on FB. Even If you only had one Adsense site, how do you know the Adsense clicks are coming from FB traffic?

If i were you i would monetize it with affiliate products.

I have never supported using paid traffic on adsense, better to gamble or play the lotto than do that..

I can't imagine that sort of arbitrage paying off, adsense revenue from a wallpaper site has to be relatively small,no more than 1 cent per visitor average, I don't know how much Facebook ads prequalify visitors to click Adsense.
Have a pinterest page, their gallery style would seem a natural, particular those cutesie girly images?

I guess it is against their terms and conditions to drive traffic from a certain source, they allow only traffic from legit serps otherwise your adsense account may get banned for violating their policies. Even though try your best to monetize from your site.