No Language on High School Transcript?

No it won’t. I agree with @lookingforward

But, and this is a big but, if the HS requires FL for graduation, it is up to the HS whether taking Arabic outside of school will count.

You don’t. In the first place, you won’t be fluent; Arabic is an extremely hard language to learn, and 4 years of HS Arabic, even if intensive with a tutor, will not achieve fluency. However, colleges do not ask you to “prove” your language skills. Once you get to college, they may have a placement test that will allow you to place out of the college’s language requirement (if they have one).