To increase both query and indexing performance, you may choose from 2 approaches of scaling out techniques: 

Replication 

Replicate the table’s content among DB instances. The data is replicated and identical on each DB instance. The full-text query can be answered by any single DB instance reducing time and network resources. Using the replication approach you minimize the number of search requests to single server / db instance. However, the modifications have to be applied on all db instances, which mean that disk, memory and CPU resources are not used optimally. The approach is similar to “master-slave” replication. In order, to replicate the table do not set PARTITION keyword when creating DB table. 

Data distribution/partitioning 

If partitioning column set, the DB table’s rows will be distributed uniformly. For more info go to: The Partition Column and CREATE DATABASE. Then each full-text index on separate DB server maintains “own” set of documents. Disk, memory and CPU can benefit greatly from smaller dataset. Speed of data modifications will increase linear. The searches increases too, however, there can be potential network bottleneck if SQL fulltext request requires accessing all db instances. Although, the problem may be seen only if number of requests go above 1000-3000 /sec.