I'd say: it depends. If every single tweet is super important for your use case, then it will be safer to store them in a datastore (whatever it is: a database, a file system, S3...). It's easily doable with Logstash: collect with the twitter input, send tweets to elasticsearch and S3.
You just need to understand that this requirement will cost you more as you are basically storing the data twice. Note that Twitter is somehow a datastore, so you can may be just use it if any tweet is missing at some point.
If the requirements are not that strict, then you can totally use elasticsearch only and avoid lot of additional costs.
Elasticsearch has backups, replication... So that might be enough to limit problems if any.
Apache, Apache Lucene, Apache Hadoop, Hadoop, HDFS and the yellow elephant
logo are trademarks of the
Apache Software Foundation
in the United States and/or other countries.