Absolutely. If you are not sending bulk requests in parallel across multiple connections to Elasticsearch that lack of parallelism is likely your bottleneck. When I have run benchmarks I have always required multiple parallel indexing jobs to saturate Elasticsearch. Exacty how many parallel tasks are ideal and what the optimal bulk size is will depend on your cluster, data and sharding strategy as well as what other load the cluster is under, so this is something you need to test.
You can see this recommended in the official documentation.