Think about this question another way:
- You are making vanilla infused liquor, you just happen to be cooking with it. And Yes, you can infuse any liquor
If you want to use a substitute for Wodka brand Vodka (i.e. use cheaper, off-brand vodka like Kamachatka), I would say that yes, you can substitute out one vodka for another with the caveat that you will want to consider the purity of the distillation you are using as it may impact the flavor of your extract. Substituting top-shelf vodka for "well" vodka may result in an inferior extraction.
If you are asking whether you can use some other grain alcohol other than vodka, itself, the answer is that yes, you can. You can even use brown liquors and so on; bear in mind they will all extract the oils but will carry the flavors differently (vanilla infused bourbon doesn't sound half bad). In particular, I would recommend going with a neutral grain spirit like Everclear; I have used it in making lemoncello, orangecello, and homemade Kahlua and it is pretty effective in extracting flavor while having none of its own.