I have tried this recipe without boiling the bagels and yes, it will work, but the bagels will rise way more in the oven (so you will loose the distinctive donut shape) and the crust won't be as chewy. Traditionally, bagels are first boiled before being baked in order to gelatinises the wheat starch on the exterior of the dough. This creates the typical chewy exterior texture with soft interior crumb, as well as a nice shiny crust.