Would it work at all?
That is, would "it" function even partly, or was it completely broken (if "it" is a device) or completely hopeless (if "it" was an idea).
In general, in most dialects, the "at all" can be replaced with "even a little", and assumes that the answer is either "no" or "just a little bit".
It comes from using "at all" in statements to emphasise a lack:
That wouldn't interest me at all.
The "at all" here adds emphasis to the lack of interest, not only would the topic not interest the speaker, but they don't even have a tiny amount of interest.
Some dialects use it as a more general emphasis though, either just to raise the attention on the question, (especially if one of personal opinion) or to express puzzlement as to the answer (especially if one of fact), such as this quote from Father Ted:
God, Ted, how did the sergeant catch Father Jack at all?
Now, Father Ted is a comedy where the writers favour some Hibernicisms because they sound funny even to those who'd use those same turns of phrase, and their dialogue is sometimes more stereotypical than realistic. It is still sometimes used informally in Irish dialects, to varying degrees.
So, in those dialects you can use it with almost any question to express puzzlement or just as general emphasis. Otherwise you can use it when the answer is one of degree, and you're already led to believe the answer will be either "no, not at all/not the slightest bit" or "just a very small amount".