Depends on the bird. I once tried a remote doorbell on a bird table to scare off large birds (pigeons); by about the third press they learnt to ignore it.
In this case could be geese, which seem more cautious (then again if it's corvids, they'll probably figure out how to reprogram the robot).
It doesn't take very much to permanently scare a bird away from a nest they're in the process of building. They're much more sensitive to threats when establishing a nest.
I was actually thinking of pigeons/doves when I wrote that. Every year I get several nests around my property and if I get too close before there are chicks, the pigeons abandon the nest.
I have to carefully track them to figure out which nests belong to mockingbirds and which ones belong to pigeons so I can chase the former away and let the latter do their thing.
Mine were happily doing their thing even while I started the same balcony. Eventually I started sterilizing their eggs by cooking and placing them back (they do leave for a few minutes when actively shooing) and after a few failed clutches they are noticeably less eager to try again in that place.
Have you tried scaring them away before they lay the eggs or is it the same result? I never noticed eggs in the nests that were abandoned (I would put them in an incubator if I did)
The term "pigeon" refers to the whole Columbidae family with over 300 birds so YMMV. Mine are specifically mourning doves which are different from the pigeons I associate with cities (feral domesticated rock doves)