What do you mean by “public AND private cloud”?
The root server and the majority of the systems that need to connect to it directly should be on the same network, but you should have relays that are behind the WAN links of your major offices that connect to a relay in the cloud if you are going to do this, just be careful of the fact that you might be paying for incoming and outgoing bandwidth to the VMs hosted in the public cloud. You can set your relays outside of the cloud to do direct downloads to partly mitigate some of this traffic, but it will still be something to consider.