Does adding a capacitor with a transformer makes it a LC filter?
A transformer is "just" two (or more) windings that are constructed in a way that they are coupled via induction, that is they are inductors.

As such you can arrange a capacitor with one of the windings in an LC configuration, and it will be an LC filter.

For a good approximation of its behaviour (e.g. to input into a simulation), considering the coil inductance is usually good enough.