Is it possible for pubertal gynecomastia to go away naturally?

Yes: Most of pubertal gynecomastia regresses within 2 years.

Possible, not likely: Pubertal gynecomastia, if it goes away at all, goes away toward the end of puberty. If it's been present for more than a couple of years, it's probably not going away without surgery.

Yes : Most cases of pubertal gynecomastia dissipate with time. If persistent, it is often best treated with partial excision of the prominent glandular tissue as well as liposuction surgery of the peripheral chest area. If the prominence of the chest wall is caused by adipose tissue, then liposculpture surgery alone may suffice.