You absolutely can, but it's not going to be easy, forty fathoms is pretty deep. The problem with mooching this deep is keeping you bait where you want it. Depending on current, you're going to need a lot of weight, I would guess no less than 8 or 10 oz, and a lot more if the current is pulling hard. I would also suggest going with a cannonball shaped weight instead of a crescent sinker, as cannonball weights get your bait deeper ounce for ounce. Also, concentrate your efforts on the tidal transitions as the moving tide falls away to a slack, and as slack starts moving. Not only are these times when Chinook bite most readily, but it will also be easier to keep your bait near the bottom.
If you aren't able to drop your rig all the way to the bottom, go with a heavier weight until you can. Some creative boat handling to match the current drift can also help keep your bait near the bottom.
A final note: Kings can pull had and make some serious runs, so if you're mooching in 300' of water, and assuming you are fishing with some amount of angle in your line, you're going to need a reel with a very high line capacity, I'd say 250 yds minimum.