The Earth would have a thin red ring around it, where sunlight is scattered by the atmosphere, right? Would the corona of the sun be very visible?
It would look a lot like this:
These images were taken by the SELENE (Kaguya) probe in Feb 2009 during a penumbral eclipse. They were not taken from the surface, but from a 50km orbit. Because of the negligible atmosphere on the moon, I assume there wouldn't be much difference. You can find other images in their gallery.
NASA have already produced their impression of what it is likely to look like. Sciencenotes.org has this picture from NASA's Scientific Visualization Studio
And if you want to see a full animation, NASA Scientific Visualization Studio also has this.
From their work it appears the corona would be very visible as with the Earth blocking out all direct light, the eye will be able to make out the faint corona. It is, after all, the principle by which various solar observatories work. The red ring around the Earth also should be obvious - it is the sun's light being refracted through the Earth's atmosphere.
I did find this artist's interpretation and a discussion at Earthsky