I am looking for a Wireless solution to our Company, the Company itself has it's base in denmark and some minor departments over seas in fx usa India etc. the question is are there connectivity to our local resources if wan goes Down ?
In principle: yes, you still have connectivity to local resources. The functionality of the Aerohive Access Points themselves are not dependent on any additional components (especially a Controller, as there isn't any...).
Having said that, you need to make sure, of course, that certain network services are still accessible and functional - same as with switches for wired connectivity. If you are using an open or WPA2-PSK protected SSID, you pretty much don't have to worry about anything. But if you use 802.1x authentication, you have to make sure that all upstream services and dependencies are accessible. Particularly your Radius server, DNS and NTP.
Otherwise, you do not lose any functionality (e.g. secure fast roaming, etc).