it'll depend on whether Neji's Jyūken could penetrate or pass through Kimimaro's bone armour. Given how Neji was unable to penetrate Kidōmaru's Nenkin No Yoroi , I don't see why he'd be able to go through Kimimaro's bone armour. I suppose you could make the argument that Nenkin No Yoroi doesn't involve Kidōmaru's chakra, merely his body fluid but the standard argument that Jyūken destroys all chakra-made substances doesn't hold up here because Neji was never able to physically eradicate the webs in the first place. The web still exists.
However, he was able to cut through the webs due to his ability to destroy the chakra circulation inside Kidōmaru's webs, rendering them ineffective. What made the webs sticky and strong was the combination of the chakra circulation and Kidōmaru's body fluid. This is obviously not the situation with Kimimaro. The bones aren't hard because of chakra. They're hard because they're bone and Kimimaro's Kekkei Genkai, Shikotsumyaku , merely propagates and controls their growth. It doesn't enhance the bones to make them stronger with chakra (although the databook does mention control of bone density. Nevertheless you get the point. The hardest bone he takes out of his body is the Spine - that alone shows that he's not creating some mystical substance out of chakra but using chakra to control the growth of his bones.)
At the end of the day, Neji's hand is still going to hit solid bone, it's not going to suddenly weaken because chakra no longer runs through it.
Thus, if Neji can penetrate Kimimaro's armour, he could have a decent chance at beating Kimimaro.