You can't "pay up" to be Plat; most (not all) years AA allows existing Plat members to renew their status by "paying up" otherwise you could "challenge" Plat as long as you haven't done it within the past year.

Plat/Sapphire lets you do advance seat selection on BA metal, and of course if AA awards elite bonus miles on partner flights (QF, CX, IB etc.) then as a Plat you'd get 100% mileage bonus instead of 25%.

But in terms of lounge access, etc., it wouldn't make a lot of difference while you're traveling.