So perhaps a better question should be: can you really say you do the complete TJQ without knowing the above weapons?
We can never understand taijiquan as they did in the old days. We live in another time and culture - in a world much much different the old. So what is complete understanding? Everyone sees only parts of a whole. Together we can complete each other, understand more from each other, but "style" as an absolute complete shape, is abstract. Striving for a full understanding of a complete art is something imaginary, a fantasy which will never be reality.
If the statement above is true, then is it better to strive for something gone in the past, then to strive to adjust or even change the knowledge so it will suite your own personality and the world you live in? Should style practice be equal to sentimental nostalgia, or a way to live and act in the 'now'.
With that said, is weapon important? Yes and no. Weapon practice will change your experience of balance and leverage. If you think of weapons as tools, then I believe they can teach you many important things. But are they important for "complete practice" or better understanding of "taijiquan"? I believe they are not very important in this matter. They can be helpful, but not much more than that.