Yes, this is exactly how a multi-region installation of Apigee works. Once the new instance/region comes online, it will synchronize with the other. Apigee takes care of all the replication for you, so there is very little to do in that regard.
The steps on exactly how to add a new instance vary depending on the version of Apigee (X, hybrid, Edge, or OPDK) you're running, but conceptually the process is the same, and synchronization works in the same manner.
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