Can retrospective damages can be sought in states designated by a PCT application before a national phase application is granted?
It depends on the country, as this is not the subject of any international treaty. I will therefore talk about the US, UK and Europe, as you referenced these in your question.
Provisional rights are defined by 35 USC § 154(d)(1), which makes an explicit reference to PCT applications. This is further explained by 35 USC § 154(d)(4)(A), which provides:
The right under paragraph (1) to obtain a reasonable royalty based upon the publication under the treaty defined in section 351(a) of an international application designating the United States shall commence on the date of publication under the treaty of the international application, or, if the publication under the treaty of the international application is in a language other than English, on the date on which the Patent and Trademark Office receives a translation of the publication in the English language.
Thus, once a PCT application designating the US is published, provisional rights may be triggered, providing it was published in English (or a translation is filed), and the other usual requirements for provisional rights are met.
The Patents Act 1977 s 69(1) provides that a patent applicant will have the same rights as a patentee for damages from the date of publication. Subsection 2 sets out that action can only be taken after grant, and that the published claims must have been infringed.
The Patents Act 1977 s 89B(3) provides that PCT applications shall be treated as published for the purposes of s 69 if they are published in accordance with the PCT and they are in English (or a translation is filed).
EPC art 67(1) provides:
A European patent application shall, from the date of its publication, provisionally confer upon the applicant the protection provided for by Article 64, in the Contracting States designated in the application.
Article 64 sets out the rights conferred by a European patent. Thus, these articles in combination provide that an application may have the same rights as a patent.
Paragraph 3 provides that the publication may be required to be in an official language of a contracting state, or such a translation has been filed before the rights apply. Paragraph 4 provides that provisional rights retrospectively do not apply once an application is withdrawn or refused.
However, because the precise implementation is left to contracting states, who are given some leeway in implementing this (by paragraph 2), it is possible provisional rights may be more or less available in some states. Without considering the case of each state individually, I could not be more precise.