I have a tasmanian oak mash paddle which has not had a finish applied, so far it has done about 10 brews. It's not the most stunning timber but is easy to work with, finish-wise it looks fine and hangs as a decorative piece in my bar when not in use. I bought some raw linseed oil to finish it months ago but don't think I'll bother now.
I've got a few lengths of celery-top and huon pine that I'll be shaping into paddles in the near future, I have no intention of sealing it with anything.
Like others have said... if you're concerned let it sit in some boiling wort or boiling water for a while.