Hi Pauljacobhall,
Presently, Office 2013, Office 2010 SP1 and Office 2007 SP3 are supported in Office 365 environment. So, if the local Office version meets the requirement, it is not necessary to upgrade to the new version. However, for some new features, it may need the latest Office version.
If you subscribe a new Office 365 plan which include Office Professional Plus license now, only the latest version Office application is available.
In addition, here is an article about software requirements for Office 365 for your reference: http://office.microsoft.com/en-in/office365-suite-help/software-requirements-for-office-365-for-business-HA102817357.aspx.
Thanks,
Eben Liu