Unless he fights Ichigo, probably. Or Bach. Which might be very dangerous, as he might end up wanting to keep him alive to keep fighting him. Which would be a very interesting twist, a pretty unique reason for a "good" character to keep the BBEG alive.

I'm guessing the 2nd-10th Kenpachis were all "unofficial" ones. The second one just took on the title after Unohana fought Zaraki and ended up passing it on to the third and so on. It's just that Zaraki is the first one to be really worthy of being the true second Kenpachi.