It would only be possible if one of the Greek NT websites allowed you to access the text via a public API. If and when that happens, or when any other versions follow the ESV’s lead, I will try to update the plugin.

For the time being, you might want to check out the e-sword.net and zhubert.com websites which should help you to get hold of Greek text you can cut and paste into your blog entries (although you will have a bit of a challenge making sure the font works correctly).