If you can get near light speed travel, then time dilation means that you won't experience a 200 year trip, only those you left behind. So any species venturing on a one-way trip wouldn't even blink at the prospect of light speed getting in their way.
I'm not a physicist, but as I understand it, it takes light 1 year to travel 1 light-year.
If the nearest life-bearing planet is hundreds of light-years away, even if you could travel at the speed of light, it would still take you hundreds of years to get there, from your frame of reference.
Time dilation just means it would appear to take even longer from the frame of reference of those you left behind (or those you were headed towards).
