If your bag is tagged through to your final destination, you will be fine. We did this a few weeks ago on Fiji and were able to use the drop-off desk at TBIT. There's a guy there that scans the bag and it just goes back into the secure area of the airport.

The key thing - the bag must be tagged through. In my experience connecting at LAX, I have never seen an AS agent in TBIT that will re-tag your bag for you. One thing about LA - they will not, under any circumstances, tag your bag through if you're flying AS on a separate ticket. The AS segment has to be on the same ticket. What this means for you is that you will be unable to re-check the bag in TBIT if said tag doesn't have your AS flight on it, and you will have to schlep the bag to T6. I've done this and it's a PITA. I wish there was a kiosk or something down there to allow people to re-tag. I believe UA, for instance, has this.