I doubt it. If he just sent the letter, it'll get to LSAC by friday/monday. Then it takes another 2 weeks. So you're looking at like Nov. 1st at the earliest.
I would say just apply now, and then forget about it. They will take care of the letter so you won't need to worry about it. The schools won't look at your file until the other letter gets there, but at least you don't have to keep checking LSAT to see if the letter's there and then apply when they finally do get to it.