Yes, that could potentially be very helpful for you. Research productivity aside, it's probably going to be one of your best bets to make academic anesthesiology connections before away rotations. Do a good job there and you could get one or more LOR's for your application. The connections you make will be far more important than the fellowship being a one-liner on your CV.
Then there's whatever research you manage to get published. Seems like a win-win scenario if you get one of those fellowships.
I have no specific knowledge about anesthesia but I'm pretty sure it's not so competitive that research years are commonplace.
