If Fao wasn't already an AP controlled space you could not SR there. If Fao was already an AP (i.e. British) controlled space it would not convert to Russian.
AP/British spaces do not become AP/Russian when RU units enter them. However, if Russia controlled Fao (i.e. liberated it from Turkish control) then Warm Water Port would turn it into a VP space for the remainder of the game.
Of course the Russians wouldn't just have to liberate Fao, they'd also have to have a continuous line of Ru controlled spaces back to Petrovsk from Fao: a practical impossibility.
Basically Warm Water Port can't be played as an event against an even semi-competent opponent. Move on, nothing to see here.
This is all very true (not but what I have acheived the "practical impsossibility on one occasion!). Answering the specific question, no the Aps do not gain a VP when Warm water port is played. The space is now a VP space, which means they have an extra liability to protect for the rest of the game, to reflect the prestige which would be lost if the Warm water port were captured.