To continue on from JF's well chosen words, test pilot and FTE training is about far more than just the mechanics of flying test points in a given class of aircraft. It embeds a philosophy of how to approach any given task, even if this is in a previously unknown field. Part of this flight test philosophy is an appreciation of the lack of ones experience in a given field and the training required to become proficient in it. Therefore, a graduate test pilot or flight test engineer does have the ability to perform flight testing on any type of air vehicle, although there may be significant pre-trial training required.
Have no fear - if a pilot or flight test engineer at a recognised test pilot school does not develop the skills discussed above, he will not graduate.