Indexes need to be updated every time you insert a document into the database - that's true regardless of index type (normal or text) and for that matter true for other databases too. It's also true for text search engines like Solr or Elasticsearch. Without knowing the size of your data set, the frequency of inserts and updates, size of the server you are running on, etc it's hard to give you a solid recommendation.
You can always start with MongoDB's text search feature and then if you outgrow it (due to size of the data or specific features required) index the data into Elasticsearch for better performance text queries.