Lately, I have been troubleshooting quite a bit in Project Server 2013's PWA and Project Pro 2013 using Act as Delegate when in PWA.
I quickly discovered I was unable to connect to PWA using Project Pro 2013 if I was in a delegate session.
I would receive the following message, "Project was unable to establish a connection with http://projects.contoso.com/pwa". This could be caused by a loss of network connectivity or inadequate permissions to connect to Project Web App."
I hope others find this information useful.