Yes, except you are 100% in control of what goes on on your server and could easily falsify data. The _whole_ point of cryptocurrencies is to avoid that.
A private blockchain spread across for example, several organizations, may be a good vehicle for sharing a database in such a way that all parties know it can't be falsified.
For example, you could use a different consensus algo and enable each organization to have one vote, one mine and this would enable sharing of data that you want to ensure hasn't been modified.
This model could connect possibly thousands of different organizations together with a trustless setup.