Question: Is "if at all" of the following understood as "(even) if the new law helps new immigrants at all"?

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> The new law will fail to help new immigrants significantly, **if at all**.
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I'd appreciate your help.

Answer: 
What is ellipted in that concession is "if [the new law...helps them] at all".

With **fails** it is a little "off". But the polarity is

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> The new law will not help immigrants significantly, if it helps them at all.
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Stylistically it would be clearer to write it that way, or like this:

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> The new law will offer immigrants little, if any, help.
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You are correct. The sentence means that the new law won't be able to help new immigrants a lot. Maybe it won't help them at all