Is membership in the Paris Convention for the Protection of Industrial Property required for other special agreements such as PCT?

Question

I am currently studying for an exam in intellectual property rights and read that the Paris Convention for the Protection of Industrial Property is a umbrella agreement, whereas agreements such as PCT (Patent Cooperation Treaty) or MMA (Madrid system for the international registration of marks) are special agreements (within the umbrella).

Therefore I wonder if membership in the Paris Convention for the Protection of Industrial Property is a requirement for any of the before mentioned special agreements and if not why?

Special agreements are mentioned in Art. 19 of the Paris Convention.

Answer 1

For the PCT, yes. Under Article 62 (PDF, pg. 47):

(1) Any State member of the International Union for the Protection of Industrial Property may become party to this Treaty [...]

For the Madrid Agreement, yes. Under Article 14:

(2)(a) Any country outside the Special Union which is party to the Paris Convention for the Protection of Industrial Property may accede to this Act and thereby become a member of the Special Union.

For the Berne Convention, no. I don't see a reason either, as the Berne Convention deals with copyright, while the Paris Convention deals with most other forms of IP. Under Article 29:

(1) Any country outside the Union may accede to this Act and thereby become party to this Convention and a member of the Union. [...]