You the end-user won't be using Postgres; you'll be using the application. The important question is whether Postgres has the features you need for your application.
My question is whether or not such set up is possible with PostgreSQL?
Are you asking if you can do with PostgreSQL what you currently do with the existing database?
Why am I interested in PostrgreSQL? First, my work has made me aware of how precious open source tools are. Our main tools for data analysis are open source. Commercial equivalents are black boxes which we try to avoid in the name of science reproducibility and transparency. Secondly, the commercial software we are currently using is apparently based on PostgreSQL, so I am hoping that using PostgreSQL will make migration less painful.
If you're already using a Postgres-based system, then the presumable answer is "yes, it'll work". However, Postgres can be modified by closed-source code, so the amount of work needed by programmer you hire might be extreme. We don't know because we don't know what your application does.