My puggle doesn't shed very much at all. I mean if I have black pants on and she lays on me-then yes but it is really very minimal. I don't ever see it on my couch or my floor, although, I do vacuum every day!
It is hard to generalize all 'Puggles' to that answer, considering each is different. Some may take coat wise more after the Beagle, which are not big shedders, or the Pug, who are heavier shedders. So it depends really on your particular dog.
Since neither the Pug, nor the Beagle have the hair / coat that keeps growing, like a Poodle or a Shih tzu, I would have to say that yes, they do shed. Dogs usually shed in the Spring and the Fall, depending upon the climate. All of their hair will fall out, not at one time of course, and be replaced with new hair, up to 2 times per year.