What is accreditation?
Major governments de-facto accredit TP schools by spending enormous amounts of money to send their pilots there. The same to a lesser extent occurs with FTEs.
The major military schools (ETPS, EPNER, USAFTPS, USNTPS) recognise each other's competencies and thus effectively create a cross-accreditation.
SETP accept attendance at certain schools as part of evidence towards membership, but it's only part of the evidence, and in any case not mandatory. Ditto SFTE and FTEs.
In the meantime, the majority of FTEs and a great many excellent test pilots function very competently without having attended a TPS, so it clearly isn't essential for *most* flight test roles (it's probably been a few decades since any TP on a new fighter programme wasn't a TPS graduate, providing an exception to the rule).
And even TPS graduates may not be suitable for any role. To pick an extreme one, an excellent TPS graduate with a background purely on high performance military aircraft wouldn't have much idea about how to tackle the flight testing of a new prototype low-performance puddlehopper built and supported by a one-man-band company, the skill-set and role-relation are (almost) totally different. [Although in either direction I suspect it'd usually be easier to take a good TP and teach them about a new aircraft class, than a good pilot on class and make them into a TP.]
So, it's IMHO an un-answerable question, except in certain narrow circumstances (such as qualification to flight test a new NATO fighter), generally the organisation needing to test something takes the best available pilot to do the job and ensures they have sufficient training from somewhere That may be training on type/class for a good TP, or (slower) in test flying for a good operational pilot.
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