Basically, yes. But it's not just the vascular system. A lot of those cells are carried in the tissues between other cells, either in the lymphatic system, or just in the intercellular spaces. Others get TO the site of injury via the vascular system.
We're all familiar with the television CSI who takes one glance at a body and pronounces injuries as being pre or post-mortem. And while obvious bleeding, and its pattern, extent, etc may certainly give a lot of information on the macro scale, most of the real decisions are made at that microscopic level in the lab after the autopsy.