Does this mean it is possible to study C FIRST and THEN 'add' C++ ?
You can study either in either order. C++ did not implement C 100%, there are a few differences.
if anything, is the significance of using an interpreter rather than a compiler ?
AFIK executation speed. It's a little like the difference between walking and riding in a car, they will both get you there but one will get you there a lot faster than the other.
It's nice only if you also like driving a Model-T automobile made 100 years ago.