If you look closely at some of the Pasta e Fagioli recipes available online, you see that there is a lot of variation in the recipes – no two are even particularly similar. This pasta & bean soup is supposed to be a classic, but someone better tell the world’s cookbook writers.
Of those that have meat (and several do not), the choice is pork, but it appears as pork chops, ribs, a ham bone, pancetta, prosciutto – you name it. On that basis, you can certainly add hamburger. We think you should cook it separately, so you can drain off the fat, and then add it when the soup is nearly done, so it doesn’t overcook.