Absolutely the existence of iron in FNA ramps up the pressure there to an unsustainable level. Especially if someone in Whitehall begins to realise the economic squeeze the FDR Administration is forcing “the Oyster” that was the British Empire open with.
From that point someone will realise the only way to prevent a WWI style near-bankruptcy is to limit gold & FX depletion as much as possible. Good tanks has helped a lot, but nobody from TTL knows ITL, so the US loss of Bataan will make things worse: As Corporal Jones from Dads Army asked “Is it true the only thing the US Army ever charged in WWI was interest?” Unless the US gets a victory, and soon, there will be a lot of allies muttering angrily about “war profiteers”.
When combined with this, gaining access to Sterling Zone iron that doesn’t require Atlantic Convoying becomes extremely valuable on its own, as has been noted. Vichy are no longer “mere” collaborators who are “in the way” and hosting Nazi spies, they’re effectively costing the empire shipping, lives gold, and FX.
I suspect the leadership of FNA will get an ultimatum: Algeria is going to the Free French. The question as noted before is simple: Does one of you want to challenge DeGaulle as the Leader & Liberator of France? If so, speak now, or forever hold your peace in the shadow of his “l’état, c’est moi” ego.