Can we say that the Patent Cooperation Treaty is a sub-treaty of the Paris Convention?

It is still distinguished by:

Patent Cooperation Treaty in English Patent

Cooperation Treaty, referred to as PCT, as can be seen from the name, the Patent Cooperation Treaty is a patent field an international cooperation treaty. Since the adoption of the Paris Convention, it is considered the most meaningful sign of progress for international cooperation in this field. However, it is primarily a treaty concerning cooperation and reasonableness in the filing, search and examination of patent applications and the dissemination of technical information contained therein. The PCT does not "grant international patents": the task and responsibility for granting patents remains solely in the hands of the patent offices of the respective countries seeking patent protection or the institutions exercising their powers (designated offices). The PCT does not compete with the Paris Convention but in fact complements it. Indeed, it is a special agreement under the Paris Convention open only to Paris Convention members.

The Patent Cooperation Treaty (PCT for short) is the most important international treaty in the patent field after the Paris Convention for the Protection of Industrial Property. It is another milestone in the development history of the international patent system. The treaty was signed in Washington on June 19, 1970 by 35 countries. It was implemented on June 1, 1978. As of July 2013, the United States has 148 member states and is governed by the World Intellectual Property Organization headquartered in Geneva.