Upvote:3
I have travelled from Fukuoka to Tokyo (and then NRT) on the Shinkansen lines that are available through the Japan Rail Pass. I believe it was the Sakura and Nozomi (layover at Shin-Osaka) trains I took on that trip back.
The journey from Hakata Station to where I was staying in Tokyo (Asakusa) was around 6 hours. Hiroshima is a bit closer to Tokyo than Fukuoka, so the travel time may be less.
I recommend HyperDia for scheduling, it should give you fairly accurate routes with prices. Google Maps is also useful.
I'm not going to specify if it's a good idea to take a train on a day's notice, but you can probably make an informed decision using these resources instead.