There are many bird pairs that go without nest boxes, but you can reast assured that not having a nest box is not going to prevent any activity in the egg making department.
If your hen does lay eggs, you have several choices, find some fake eggs ahead of time & substitute them for real ones as she lays them or you can shake each egg vigorously (scramble them) and place them back in the nest or you can just let nature take its course & give away the resulting chicks.
Simply removing the eggs may cause the hen to replace them, which can be taxing on her body. If you decide to try fake eggs, you need to change each egg out soon after she lays it, without letting either bird see you or they may discard the fake themselves.
