Sure it is do-able

The trip from Shin-Osaka to Hiroshima on a Hikari RailStar will take 2 hours and costs you 9440 yen one way

http://www.hyperdia.com/classic_en/hyperWeb.cgi

Most people who go to Hiroshima checks out Miyajima as well, and depending on what you want to do and see in Hiroshima, there should be time to do both. Just take the first train out of Shin-osaka and the last train back from Hiroshima