Onomichi: can i explore shikoku?

I was thinking of reaching onomichi in the morning (perhaps starting the ride at 8am), cycling over to shikoku, and exploring the coastal down.

Is this possible? Timing wise, particularly.

Depending on your cycling ability, it is very possible.
According to this site, it takes anywhere from 3 hr to 10 hr to cross the channel by bicycle. http://www.go-shimanami.jp/global/english/

How much time you will have in Shikoku depends on your riding speed.

It depends. How many days do you have? Shikoku is not just a small island. Shikoku is huge. I live in Shikoku and have traveled a lot of it. If you have a bicycle and have a lot of time, yes, you can explore Shikoku no problem. However, if you are on a tight schedule, you cannot explore all of Shikoku. If you just want to cross the Shimanami Kaido (the series of bridges and islands) to get to Imabari in Shikoku, then yeah, you can do that in a day.

As others have said it depends. If you are regular cyclist then it's easily doable. I'm about 53 and a reasonable club cyclist, used to riding 100km a day. This is my strava track from a few years ago to give you an idea of how long it took me. I took the ferry from Hiroshima to Matsuyama & then rode to Onomichi. The odd bit is where I turned towards Imabari then realised I had to keep going or lose the light. It was a great day. https://www.strava.com/activities/9941810