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Only if they can be turned off (same as the cryo sleep). The whole ship either has to have enough energy to last potentially 100000 years (no theoretical power source exists like that) or enter a state of 0 energy consumption. Solar/radiation collectors dont work if you are to far from a star. Synthetic life still needs energy
Well, that depends on how far you're going. If you pick a nice close target, let's say 3 light years away, you can potentially get there pretty quickly. With fusion propulsion systems you could make the trip is something like 70 years, coasting most of the way. I'd need to check the math to get exact numbers, but I recall fusion allowing for pretty reasonable trip times.
But if you can survive for hundreds or thousands of years, then solar sails become an option. Then it becomes a materials science problem of how thin can you make a sail that will still hold together. The greater the sail to payload ratio, the faster you go.