The short answer is no. Long answer, yes, by targeting nested elements, for example:
li:nth-child(odd) {background:blue}
li:nth-child(odd) li:nth-child(even) {background:blue}
li:nth-child(even) li:nth-child(odd) {background:blue}
But for levels 2 or 3, you probably need a lot of rules.
You can do this with javascript as well, going through the tree and increasing the counter, applying a style when the counter is odd or even.