Unit tests, by the book, are meant to exercise the code you write, isolating it from dependencies (SO calls, external libraries and even language built-in libraries if important for your code) through mocking.
What you may need is integration tests, which means checks that will evaluate if two components can communicate. They are different than integrated tests, which bundles two or more components and evaluate the output of them as a unit.
In integration tests, you rely on the unit tests of the components and exercise the communication:
Does service A send the data firstName and service B reads the data
firstName, rather than FirstName or name?
If you don't have such conviction on the unit test quality of the library or if you believe that the authors of the library will not respond to bugs in a timely manner for your project, you should surely do a small amount of integrated testing, by building your app without mocking the library and inputting some special data you want to be more sure.