Can multiple fractures of the humerus bone heal without having surgery?

Unlikely. While a single fracture that has not moved (nondisplaced) can heal with out surgery, the more fractures present the more likely that surgery will be needed to stabilize the bone.
Yes. Most fractures will heal without surgery. Surgery for fractures is generally necessary to hold bone in good alignment during healing and to allow use of limb during healing.

Related Questions

I am 22, my humerus bone is fractured and I have done surgery on18 april, 2014. The doctor installed a plate with 8 screws. When will this be healed?

Good question. You have to consult with your orthopedic surgeon who did the surgery. He/she will examine you and may also get an imaging study. That and the general state of your health will determine the extent of healing.