HGH travels through the blood and stimulates the liver to produce a protein called insulin-like growth factor #1(IGF-1). IGF-1 helps the cartilage cells located at the ends of long bones called the growth plates to multiply, which is where bone growth occurs. During puberty age, this leads to growth in the length of the bones and increases one's overall height. By end of puberty, however, the cartilage at the ends of most long bones is converted to bone this is known as the "closing" of the growth plates. Any subsequent action of human growth hormone or IGF-1 usually cannot increase the length of bones.
The question of whether you can grow taller with increased supply of human growth hormone is only relevant if your growth plates are still opened.
What exactly is growth plate? The growth plate, also known as the epiphyseal plate or physis, is the area of growing tissue near the end of the long bones in children and adolescents. Each long bone has at least two growth plates: one at each end. The growth plate determines the future length and shape of the mature bone. When growth is complete--sometime during adolescence--the growth plates close and are replaced by solid bone
Unfortunately there is no easy way find out whether a growth plate is still opened or not, the only way to know for sure is to have an x-ray done on the bones by a doctor.
If your growth plates are indeed completely closed human growth hormone will likely do nothing for you as far as height increase is concerned. You are better off pursue other height increase methods, go to Complete Guide to Natural Height Increase, this website documents every known grow taller methods exist out there.