Serpentine belt after 3g alternator swap

So I finished up the swap to a 3G alternator last night, and this alternator pulley is slightly larger than the pulley on the stock 2g. I can fit the serpentine belt on, although the tensioner isn't released quite as far as it was before (obviously). I'm thinking since the tensioner is an automatic tensioner, that as long as I can fit the belt on without any issue then I should be good to go? I was expecting to have to buy a little bit longer belt, but it seems that regardless of belt length (within reason of course) the tension on the belt will always be the same as it's imposed by the automatic tensioner.

Am I on the right track here?

10-4, that's what I thought I just needed a sanity check.

Unfortunately the alternator I got has bad bearings it appears. You can't turn the pulley by hand, but sometimes it breaks loose a bit and when it does there's a terrible screeching/metal on metal sound.