Is it correct to use the terms multinucleate and syncitia interchangeably?
No, the terms multinucleate and syncytium are not synonymous in this context.  Most cardiomyocytes are not multinuclear. To be clear, syncytium is used to refer to multinuclear cells that originate from fusion of uninuclear cells, including the skeletal muscle, but that isn't what is referred to in the context of cardiac muscle.

The Wikipedia page on syncytium summarizes this nicely:


  Cardiac tissue is therefore described as a functional syncytium, as opposed to the true syncytium of skeletal muscle.


The "intercalated disks" of cardiac muscle are filled with gap junctions and desmosomes. The desmosomes hold the cells together physically, while gap junctions allow ions (and small molecules) to pass directly between cells, forming "electrical synapses". This allows electrical signals to propagate between the myocytes to coordinate contraction.

Gap junctions are formed by proteins, rather than fusions of the plasma membrane, so they are relatively small. This means that not everything in the cytoplasm can pass through them, mostly just ions and some small molecules. Proteins, for example, would not pass through gap junctions. Therefore, cells that are connected via gap junctions, like cardiomyocytes, are still somewhat independent, unlike fully multinuclear cells.

There are also types of neurons, including some in the CNS, that also form gap junctions and act at least somewhat in concert in this way.