And while you may be allergic to dander, and the amount of shedding can be an indicator of what to expect in terms of dander quantity, it is not a perfect method of discerning whether a certain animal will trigger your allergies. Some people are allergic to the slightest bit of certain danders in the air...others need a large quantity before they show a reaction. Exposed to enough dander (like the home of that old "cat lady" you used to know, the one who never vacuums or opens the windows) even hale and hearty folk are going to sneeze and get itchy.
It is the same with all allergens. For instance, I know a person who cannot go outside during ragweed season. It is a living nightmare for them. I, too, am allergic to ragweed, but only mildly. A bit of a runny nose on the worst days, maybe some itchiness, and that's it. So it is with dogs: a tiny bit of dander may trigger a reaction in some, while others can live on a day-to-day basis with dogs as long as they keep the house vacuumed and use an air filter.
So, although every dog sheds in some way, not all dogs shed equally. Cockapoos, in general, shed far less than most dogs. This is owing to the fact that their "fur" is more like "hair." Generally, people call dogs like poodles and cockapoos "non-shedding," but this is a bit of a misnomer, for reasons I have already explained. Actually, you are nearly as likely to find human hair on a carpet or furniture as cockapoo hair. But each dog is different, and I have heard some owners say their cockapoo loses more hair than most cockapoos.
More importantly, if you are concerned about shedding due to allergic rather than aesthetic reasons, you can rest assured that the dander levels from cockapoos are lower than many animals. However, since sensitivity levels in individuals can vary widely, it is important to acquaint yourself with a dog of the same breed you intend to buy or adopt before bringing him home permanently.
So the short answer is: Yes, but much less than most dogs, and even less than some people!