CLY isn't a center, first of all, but I understand your point. If LVP is picked, Austria and Turkey are unlikely to take it. That's why there's also the solo option though and I think a solo is quite a possibility, especially because people will be so busy trying to get to LVP.
Arguably, Austria is more likely to win through a solo than England is to own LVP in Fall 1910 because England is extremely likely to be attacked by France, Germany and possibly Russia instantly.
As far as winning goes, I think I'd rather be Austria if LVP were to become the target center.
Maybe Italy and Russia decide to move everything towards LVP in an attempt to take it at some point, leaving all their home centers open to Austria and Turkey..
Also hold in mind that a regular 'stop the solo'-attempt won't be rewarding in this variant, *unless* you hold on to LVP. So let's say Austria has 17 centers in the eastern block and the powers in the west, say Germany and France, are perfectly able to keep the stalemate line. However, France holds LVP, the year is 1908.
If Germany just holds the stalemate line like in a normal game, he doesn't get a respectable 3way draw like in a normal game, he outright loses.
That's the beauty of the game: I think it's an elegant way of getting rid of the pesky draws, by adding a victory condition that will always be achieved by someone (unless a center stays neutral until 1910, I guess then the survivors draw and that'd be so epic!) if, and only if, a solo is not achieved.