Under the original agreement Southern Iraq was be under British control and even if it wasn't it would likely be under British influence. Iran also just came out of major famineCould see Iraq partitioned earlier with a few PODs involving the Sazonov part of the original Sykes-Picot agreement managing to be realized allowing for a Russian mandate to be established in Western Armenia, Assyria and the Kurdish areas of OTL Iraq / Syria / Turkey (via a better performance by Russia in WW1 followed by a territorially screwed post-war Turkey).
Persia would probably attempt to invade the Shia part, while the British would either attempt to keep it independent or in the event of a successful British-backed Sheikh Khazal rebellion merge it with an independent Shia Arabistan (aka OTL Khuzestan Province).
https://en.wikipedia.org/wiki/Persian_famine_of_1917–1919