See this is an odd one. The IB's best showing was ordering Death around like a little dog. Unfortunately for him, he's never been shown doing anything that impressive ever again. It also makes no sense; he ordered around a being MORE powerful than his creators.
If you believe he can really go "above his pay grade" like that on a normal basis, then yes, he can beat Nekron via BFR by summoning the White Light of Creation and banishing Nekron to his realm. Keep in mind this wouldn't kill Nekron at all. It was stated REPEATEDLY, in not only Blackest Night, but the Green Lantern Corps mini AND the Captain Atom issue, Nekron CANNOT BE DESTROYED. So at best IB wins via BFR.
Now if you believe that Death fiasco was a fluke, then it's either a stalemate or Nekron figures out how to separate the IBs two halves, thus destroying him. My money is on Nekron in this scenario.
Truth be told, the IB is all over the place power wise and the character is a hot mess (like the Beyonder and MM).