This answer may be partially of interest from a previous AskHistorians post about the age of the average GI. It lays out the fact that the average soldier was actually in their early to mid twenties. The age bands listed in this post would seem to indicate that high school aged soldiers were actually pretty rare in WWII.
This answer focuses on the United States, since the question contains the term "high school."
No. Generally American military personnel whose high school education had been interrupted by wartime service did not return to high school to complete that stage of education. In many cases they would have been above the maximum age of attendance or their presence would otherwise have been difficult to accommodate in institutions designed for the education of minor children. They simply went without high school diplomas.
Instead, many of them earned the credential known as the GED, from the "General Educational Development" test. The GED test was developed by the American Council on Education during WWII to address the specific issue presented by the mass induction of young men into military service before they had completed their high school educations and earned diplomas. In particular, how would they establish they had a sufficient education to enter college? A passed GED test was accepted as the equivalent of a high-school diploma by large numbers of registrars. In addition, the GED test was accepted by many employers as the equivalent of a diploma.
Courses to prepare for the GED, as well as the test itself, were offered to military personnel. The generally favorable encounter of universities and veteran students with GEDs and the G.I. Bill in the years just following WWII seemed to validate the concept.
The success of the GED and the ACE's investment in it sidelined efforts to award "veterans' diplomas" or to accelerate high school for students likely to be drafted. These were actually somewhat popular during 1942-43. But the ACE was able to convince stakeholders that the GED was an appropriate equivalent. After the war, the GED became available to larger groups of people who had not finished high school, not just military personnel, and got pretty wide acceptance. Nowadays if a person was not able to attend high school for whatever reason, that person is almost always steered toward a GED.
The idea of awarding diplomas to veterans never fully went away, though. In 1999, a high school in Gardner, Massachusetts held a graduation ceremony for 39 former students whose education was cut short by WWII. (Fixed!) This led to a nationwide campaign known as "Operation Recognition" (after the original) whereby high school diplomas were awarded to veterans. Typically this was authorized by state law, with school districts verifying the records and awarding the diplomas. In most states the Operation Recognition statute covered WWII, Korea, and Vietnam. Arguably the emphasis here was on the social and ceremonial aspects of high school graduation, but as far as I know the diplomas awarded are real academic degrees.