Instead of adding default value , you can adjust it in the query using missing filter. Lets say , you want to search based on a match query - Instead of just match query , use a bool query with should clause having the match and missing filter. inside filtered query. This way , those documents which did not have the field is also accounted.
If you absolutely need the value in that field for existing documents , you need to reindex the whole set of documents. Or , use the out of box plugin , update by query -
