First off I think finding such a body would be an extremely low probability event. But, assuming you find one going in the right direction you have to have everything you're taking along match velocity with it. If it's going at a speedy clip then somehow you have to get up to the speed of whatever you're riding on otherwise you have the bug hitting the window of the jet plane effect. Then there's the problem of the other end. How do you slow down enough to avoid making a kinetic energy explosion dwarfing the size of the KT boundary event? I would say that the devil is in the details, but these aren't details. They're the major components of your proposal.
That is if we wish to send people. If we only send DNA, in the form of some sort of organism (water bear, bacterium, or even viruses perhaps) then a lone craft of much smaller size would probably be the best alternative.