The racial hit dice of the lycanthrope template (2 in the case of a werewolf) count towards your level for Vow of Poverty. The level adjustment (+2 in the case of an afflicted lycanthrope), however, does not. This is because Vow of Poverty refers to “level” which is synonymous with “hit dice.” Racial hit dice, unsurprisingly, are hit dice, as are class levels, but level adjustment explicitly offers no hit dice. The only thing LA affects is what level you count as for the purposes of meeting the requirements of a new game (i.e. if your game starts at 5th level, your LA +2 would count against that limit), and then from there the XP needed to level up.
That said, please note that Vow of Poverty is an atrocious feat. The statement in Book of Exalted Deeds that the feat provides “certain spiritual benefits that can help outweigh the lack of those items” is flat-out false—a character with Vow of Poverty is always, 100% of the time, weaker than one who has all the wealth he or she is supposed to have at their level.
On top of this, level adjustment is very, very bad for you, and lycanthrope as a template does not nearly provide value sufficient to justify its adjustment. It is, in general, also a very weak choice.
And to top it all off, the two do not synergize well at all. Vow of Poverty works best (least badly) when you have magic of your own to offset the lack of magic items. Lycanthrope, with its hefty RHD and LA, makes being any kind of spellcaster a poor proposition—but that means your class lacks magic, and the Vow prevents you from buying magic, and that is very, very bad—D&D 3.5 is absolutely dominated by magic.
Now, you are certainly welcome to choose to play an exceedingly weak character, so long as your party and DM are OK with that—but you need to do it with your eyes open, aware of what you are getting into. Not only may it provide a very frustrating experience for you, it may also annoy your fellow players if you feel like dead weight, and it may furthermore cause headaches for your DM, as he or she tries in vain to find a decent way to equitably challenge all of the members of the party when one is as weak as your character will be.