It could, but it would be pretty expensive probably. Storing information on-chain is costly, so you don't want to do it unless its absolutely critical (the information you want to store needs to be totally and absolutely incorruptible). If you already have a server-less architecture set up for sharing the database doesn't seem like you'd need to use Ethereum (which is itself a server-less architecture).
EDIT:
Just realized you said data model was the core of what you deliver to your customers. One thing I will say is that you could build the software that utilizes that data model (moves the data around) into a contract on Ethereum and then have an application that all your clients download that utilizes those functions using local data. As long as the users of your application are running an Ethereum node, they could access those functions from the blockchain essentially for free (as long as they don't change anything on-chain). That way, you can be assured that everyone is using the same functions, since they will be stored on the blockchain and incorruptible.