Yes. Any concrete subclass will have to implement the abstract methods, so they will be implemented by the time any JVM is asked to invoke the method. It's just a special case of implementing by forcing subclasses to implement for you.
Your abstract class doesn't even have to mention the methods in the interface it 'implements', e.g. the following:-
interface SomeInterface {
void foo();
int bar();
}
public abstract class YourClass implements SomeInterface {
}
is perfectly legal. If a subclass of YourClass wants to be concrete class, it has to implement both foo() and bar().
I hope this clears your confusion.
Thanks