Well, you never actually feel time dilation. It's merely an effect that changes how we perceive clocks moving in other situations. We would always see a clock sitting right next to us ticking away at "normal" speed.
But, anyway, if we were to collide with a black hole, we'd most likely be killed off by the high temperatures that result from our planet becoming, or joining, the accretion disk of the black hole (if we survive the breakup of the planet due to tidal stresses).
Much more likely than actually being swallowed, though, would be just the object passing close enough to the Earth to disrupt its orbit. Too much disruption and we'd either be cooked from moving too close to the sun, or freeze from moving too far away.
But the chances of a black hole coming anywhere near us in the next billion years are pretty near enough zero that nobody cares.