Wow! Never heard of Google themselves telling you that you've got dupes in your website. To answer your question, YES. Google will eventually pick the changes up however the only question would be when?
Updating your site is fundamental to good SEO. Google loves new and fresh content, and changing your content literally invites Google to crawl more of your site. If they keep going back and finding the same stuff every time, they'll get bored. Change something, and they'll probably start crawling everything else to see what else you've changed. At least that's how I understand it. Retail sites suffer with duplicate content because it's so hard to write something completely different from the original product description. It is vital though to make sure as much of your content is different to everything else out there.
Of course Google will recognize the changes on your site. It made not be immediately, or soon but it will happen. You will most like get an updated crawl within 3 weeks. The normal that most people see an updated crawl is around 1 week to 3 weeks.