I haven't seen much in the way of data on this. Since many usability studies and A/B tests mean that a site has solid investment, it's rare to see someone test "bad grammar" vs. "good grammar". Plus, if you've invested in good grammar enough to have a "B" version, then why not just use it. So, practically, you just don't see this in the research very much.
I agree with GNC that it's primarily a trust issue. Are you going to give your credit cart to a company with dozens of typos, spelling mistakes, and bits of bad grammar? If they offshored their copy for bargain basement prices, is that where you want to put you money?
I saw a good international SEO talk once about the importance of writing copy for your target audience and NOT just translating. So much is idiomatic that it's easy to lose important details in translation. When your competitor is a click away and especially if you're an unknown quantity (and not a big brand), these details can matter quite a bit.