Seeing the Sunrise from Sunrise Izumo?

So I was thinking of going out to Yonago to catch a festival, and then take the Sunrise Izumo to Tokyo. When I looked at the timetable it said it passes Fuji at 5am, and a quick google search says the sun will rise in Japan on that date (Aug 8th) at 4:54am.

The question is, has anyone actually seen the sun rise on Mt. Fuji from the Sunrise Izumo? That's the only aspect I'm interested in compared to a 3500 yen hotel and traveling by day on the JR pass.

I don't think that the mountain and sunrise quite line up, but I imagine that around Shimizu the scenery to the right of the train could be quite spectacular during good, clear weather.

Note however that the sections during which you can see the mountain to your right are rather short.