Absolutely. Databases are generally numeric data, linguistic data, or a mixture of both. There are kind of two variants here: NLDB (Natural Language Database), and NLIDB (Natural Language Interface to Databases). Both are related to NLG (Natural Language Generation). The high profile companies in the NLG space, such as Automated Insights and Narrative Science, are basically summarizing or interpreting numeric, linguistic, or mixed data. This is like two ends against the middle. A chat interface to a database needs something interpreted in natural language on the other end in order to interact.
For instance, I’m sitting on millions of dollars worth of data in CSV format, at today’s retail price, that I can’t talk to. One needs to make some sense of the data, in terms of insights, before being able to talk with it. Basically, I need a SaaS, preferably a visual SaaS, that I can simply upload my CSV data to, and then be able to query it in natural language via API. However, generally data, especially natural language data, needs a tremendous amount of cleaning, called Normalization. There is also de-duplication to consider. Then there are quite a few statistical/probabilistic gymnastics required to extract insights. Bottom line, real people need easy interfaces.
See also my related Quora answers: