Well, you can certainly do whatever you'd like with your wine! That's the beauty of making your own. For me, I wouldn't oak pinot grigio. That is a light, crisp, dry, sometimes fruity wine, and oaking it might overpower it and also cause it to have to age too long. Generally, it's drunk as a young wine, and I think the oak would not be good in it.
If you want to try it, though, why not?