You could still have extra lessons at an FAA school and log the hours but they will not count towards PPL minimums and you will need a training Visa (ignore the people who try and convince you that because you are not training for an FAA PPL you are somehow excused. The TSA do not see it that way).
You do need TSA clearance for ab-initio flight training in the US. There's no way around it.
As far as a visa is concerned, in your case, your primary purpose for visiting the USA is not flight training. That would mean that you do not need an M-1 visa. But there is one caveat: being cabin crew, I assume you're not entering the USA under the VWP or under a tourist visa, but under a crew visa. There might be specific restrictions attached to such a visa. I simply don't know. So don't take my word for it. Contact the US authorities directly and see what their opinion is.
But as Tall_Guy says, both the visa and TSA question is completely independent of whether you are doing FAA or JAA.