Personally I'd be much more interested in having lounge access on the LA flights rather than worrying about the priority check in which they can only verify when you are actually at the desk so why not just go for it and explain your case if necessary? I cannot tell what is the exact situation with AA and LA but with AY/BA/CX the status is visible within 1-2 days after it's confirmed by the "home" carrier.

What I find really strange here is that as you say you'll get AA Plat status on your first flight you should be an AA Gold already? That alone will give you access to J check in on all OW flights? Sorry if I am wrong here with my assumptions and I also remember that there's this Plat challenge program with AA..