The Blockchain is composed of multiple blocks that can contain any information. However, it is not a database in a traditional sense: it is not fast, and it does not answer queries.
For example, the writing speed is one block every 10 minutes for Bitcoin and about one block every seven seconds for Ethereum. Queries, as such, do not exist at all: neither SQL nor NoSQL-type language is not provided.
Meanwhile, the information stored in Blockchain often needs to be searched. Here is a design pattern from CSIRO.
As of today, such a tool exists. FreeEed has been used by lawyers to do eDiscovery, legal reviewers, and researchers for all kinds of investigations. It allows you to give any data as input (see here) and indexes that data for searches. The data can be open Office files, PST mailboxes, a "load file" produced to lawyers due to an eDiscovery request, and Blockchain.
We are actively working on FreeEed all the time, adding input formats, processing capabilities, and machine learning. The tool is open source and welcomes new additions. The review part is called "FreeEed Review" and works through the browser.
The back end used to implement text search is Elasticsearch. This means that you can also look at the processed data through the mighty ELK (Elasticsearch, Logstash, Kibana), which is also open source.
Happy searching!