I would guess that if we are technologically advanced species we will. Though there is really question could we discern those signals. Probably there would be push to maximise the usage of available spectrum and then minimize use of power and probably even look into massive mimo.
Or would we have transitioned to highly directed laser pulses, or perhaps using a medium not yet discovered? Since we are still fumbling in the dark about fundamental physics, having no grand unifying theory between large and small, or even much progress in understanding gravity, it is entirely possible that we wouldn't be using radio because we found something much better.
A small note: a Grand Unified Theory is not a theory that unifies the large and small (presumably you mean something that solves the measurement problem in QM), it is a single theory that unifies the electro-weak force and the strong force, leaving us with just two fundamental forces: the unified one and gravity. Solving the measurement problem is necessary for having a complete picture of the universe, but a GUT is not - it is logically possible for the universe to have several different fundamental forces; but it's not logically possible for the macrocosm not to be reducible to the movement of its constituent particles.
Other than as an inception agreement for a cult (has someone already written that book, other than L Ron Hubbard) 1800 years is unfortunately a very long time in the scale of any human project.
I guess it would depend on the ship... Though I am reading Rendezvous With Rama right now (my first time), which has completely changed my imagining of space ships. So much of sci-fi owes so much to Artur C. Clarke. I knew, but I didn't realize until I read more and more =/
After 72 generations on a ship, it’s possible the occupants won’t even know they are on a ship (fictionalized by Brian Aldiss in the excellent book “Non-Stop”).
And if they know they’re on a ship, why would they leave? After all, it is home and will have been for ages.
Also if you can build a space habitat that can support 72 generations. Why ship it away anyway? That is bit nasty move to those eventual descendants. Instead put it orbit somewhere in system. Where you have at least chance to maintain or rescue the people. And save a lot on propulsion. Just build enough of them house people you need.
I never understood the whole colonization for sake of colonization. In past it was either glory or better living conditions. And you will have much better living conditions if you don't send it to empty space on unknown risky voyage...