It is supposed to be nondestructive if the components were designed and fabricated properly or have not been damaged over time to an unacceptable extent, and the test temp is above the min needed for required ductility.
It will affect material properties at local stress raisers- assuming the material has the minimum required ductility at the test temperature and the vessel was fabricated properly, there will be local yielding and some degree of hardening at the stress raisers. Many simplified stress concentration factors are on the order of 2.5-3 ( can be as high as 5 at the edge of a crack), but on a microscopic scale and considering yielding and fracture mechanics, the high stresses result in local yielding and not component failure.
Failure would occur if there was inadequate ductility due to too low a test temperature or incorrect heat treatment such that there was nill ductility, or if the component was not designed or fabricated correctly. The failure due to nill ductility is a rapid progression of the crack, and if it is massive component, can lead to serious injury to personnel who are directly under or alongside the vessel. It sounds bad, but could be much worse- if you were to pnuematically test the vessel and it failed with nill ductility the result can be an explosion and damage within a wide area of teh vessel.