Reposting this from our Sustaining Engineering Blog since it applies to Project and Project Server as well. The Office 2010 June 2013 CUs will not install on Office 2010 SP2. You can, however, get the changes in the June 2013 CU in addition to the new ones in the Office 2010 August 2013 CUs. We are working towards a scheduled release date of August 12, 2013. That date could change should we find an issue we need to fix before we can release it. Of course, we work hard to make sure that it will release as scheduled as we realize the impact delays have on our customers.
Sustaining Engineering Update:
Thanks to Anil for point this out!