Yes Boxer dogs can shed a lot of hair especially if you do not groom them enough to keep their shedding hair off of them.
If you brush the boxer dogs fur often then the fur won't get all over the place when they shed their fur.
Just like many other dogs boxers will shed their hair and you just need to keep up with grooming and brushing them and the fur won't build up and fall off over everything.
I had a boxer dog and had to brush and groom him weekly to keep him from shedding his fur all over the furniture and bedding.
He loved to sleep with me so I had to keep him groomed so that the fur would not get all over my bed.
He was a loving dog though but the shedding hair is hard to deal with.