part answer to your question is yes.
after soviet mobilization (DE-SM, see 20.55 for the large number of negatives against this), the reds could DOW Persia.
even though it is considered a 'British protectorate', I'm sure if the Brits can DOW their own protectorate - so can Russia.
as for your Production Point part of your question - NO.
middle east PP's stay British , even if red occupied - nice try there.
20.921 British Protectorates
Iraq and Persia are Cooperating (16.0) with the Allies: they have ceded PPs, Bases and Transit Rights (see below) to the Allies while still remaining 'neutral'. Even when occupied by the Soviets, they are considered to be Allied controlled.
and all this is probably redundant anyway, because in the version of the rules to come out next 1.16 , Persia will not be allowed to DE-ME (Persia) until Russia has Mobilized/or been invaded .........
roll on ..........