It is rare for a HotCore bullet to "come apart" in the traditional sense, considering that the core is permanently bound to the jacket. These bullets usually produce smaller mushrooms and do not over-expand - they give deeper penetration than conventional jacketed bullets. However, I have not used the .308/200 Speer HC so I do not know for certain. From personal experience, the .338/200 Speer HC does hold together and penetrate well on caribou at .338 Magnum velocities (ca. 3000 fps). Ditto the .277/130 Speer HC at 3100 fps on deer.
Few if any game bullets will come apart in flight; the bullets which do so are very thin jacketed varmint bullets fired at a velocity too high for their jacket strength. 3000 fps is not very fast in today's shooting world.