Yes, it is possible. However, the question is very vague so it's hard to give a specific answer.
That being said, you could create a core data model class, and that class could contain code to 'synchronize' the data with Firebase - there's many ways to sync your data.
Depending on your use case, you may want to consider looking into Firebase as a single datasource instead of going between the two.
And yes, use Swift.