This is a good plan and I have found that watercress grows well in moist soil, being invasive too as its shallow roots spread laterally and then form new clumps. But it has little frost resistance when grown in soil, though late spring frosts may be tolerated.
I expect you know land cress which is excellent for winter and similar in flavour. Mine, sown late August, is cropping heavily at the moment – even without protection and pigeons normally love it – and should continue until flowering in early May.
The dove poo should not be a problem as water is passing through soil forst and being cleansed by bacteria.