When performing changes in Active Directory, Adaxes Service connects to the nearest DC available. Thus, if you install an instance of Adaxes Service in the remote site, it will connect to the local DCs and perform the changes there. Then, those changes will be replicated to your main site via normal AD replication.
As to changes in Adaxes configuration, Adaxes uses an instance of AD LDS as its configuration storage server. Adaxes configuration replication is made by means of AD LDS replication. It is very similar to AD DS as they are based on the same engine. Thus, if the link goes down for several minutes or hours, this should not make a huge issue. The only thing we would recommend is to track the AD LDS logs for lingering objects and failed attempts to replicate, the same as you would normally do with AD DS replication.