Yes, they will go out of sync, probably fairly quickly, too. If their cycles are not too different in speeds and they don't store their last position in the cycle, you could try hooking the power for the LED's to a microcontroller and briefly interrupting power to them at an appropriate interval (time how long a full cycle takes up and use that as an interval). That should reset them to start the cycle again at the same time. You will probably notice the "blink" when they reset, though, unless they start their cycle dark and there is another point in the cycle that is dark that you can use as a reset point. You can experiment with how long they need to stay off to reset the cycle.
AFAIK, there is no way to send them some kind of timing signal to keep them in sync otherwise.
I agree on all this.
Just a suggestion: if you have enough space to put two leds instead of one, you can always solder two of them everywhere in opposite directions. Only one will lit. By changing the polarity on a regular interval (inverting VCC and GND), you'll trigger a cycle for the other set of diods. This way, you can probably have a very stable cycle (just set the inversion at an interval equal in length with the cycle) and no blink/black state.
(just check before that they can be put in reverse, like any other diods, that may be different for this kind of diods with electronics inside)
