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If somebody makes an Ad HominemYou Fail Logic Forever argument like "Charles Darwin was racist, therefore evolutionary biology is false" and I counter with "By the same logic, the Nazis discovered that smoking causes cancer, therefore 'smoking = cancer' is false", have I lost the argument thanks to Godwin's Law?
Only amongst people who misquote Godwin's Law. There is nothing inherently wrong with referencing Nazis in an argument, and Godwin's original statement never said that there was. Any place that imposes a rule of "if you mention Nazis, you lose the argument" is making a lazy generalisation, on the basis that Nazi comparisons are usuallyAd Hominem attacks on your opponent.
Here's a simple rule: If Hitler/Nazis are relevant to the discussion it's not Godwin's Law. If Hitler/Nazis are used to demonize or insult the opponent it is. In that case it's making a comparison using the same logic as the other person.
Godwin's Law is an all-purpose shutdown. When someone uses it in a conversation unrelated to the Nazis or WW 2, it's a sign that the person is out of arguments and basically has lost the discussion.