Can I invoke Google to check my robots.txt?

You can't make them re-download your robots.txt when you want them to. Google will re-crawl it and use the new data whenever they feel it is appropriate for your site. They tend to crawl it regularly so I wouldn't expect it to take long for your updated file to be found and your pages re-crawled and re-indexed. Keep in mind that it may take some time after the new robots.txt file is found before your pages are re-crawled and even more time for them to reappear in Google's search results.