I would always upgrade to the latest version because the code is always more secure and more stable than previous versions. One action that many would always agree too.
In regards to the theme, well I guess you would not know until you upgraded WordPress. I would let the website owner know that the theme might not function well with the new WordPress version. I have a client who likes this theme and it was designed many moons ago and has not been updated for the last 2 years or more and it still works well under WordPress 3.4.1. However I am not very happy running an old theme unless the code is updated. I would rather use a current theme and tweak the design.
The plugins must be updated to the current version. The code is always vulnerable and open for hackers who love old code. You must always try to limit the possibilities for hackers.
BEFORE you go ahead, make sure that you have a current BACKUP this is extremely important.
I would also find out more about the plugins and when was the last time they were updated. Then workout which plugin to update first before you update WordPress.
Also you should close the site down with a nice currently is under construction page while you do all the updates and or upgrades.