Is "if at all" of the following understood as "(even) if the new law helps new immigrants at all"?
The new law will fail to help new immigrants significantly, if at all.
I'd appreciate your help.
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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
The new law will not help immigrants significantly, if it helps them at all.
Stylistically it would be clearer to write it that way, or like this:
The new law will offer immigrants little, if any, help.