While waiting for a complete answer, you might be interested in this discussion of the grammar of "I am become death." It's seven years old and I still think about it all the time. /u/yodatsracist and /u/mercurialohearn might have more to contribute now.

Other comments link to previous answers about the meaning and use of it, but on the question of "would it have been commonly understood by other (Western) scientists?" the answer is, no, probably not. There were some theoretical physicists who had an interest in Eastern philosophy other than Oppenheimer — it was seen as a potential well-spring for inspiration when thinking about concepts that got outside of the typical mechanistic, "classical" physics that had dominated the Western tradition — to my knowledge there were not that many who took it as far as Oppenheimer did. Oppenheimer learned Sanskrit from one of the great translators of his day, and the translation he gave was his own (and varies significantly from other translations).

Oppenheimer had two affectations that are worth noting because they seem to have an apparent dissimilarity but probably come from a common origin. One is the deep interest in Hinduism — not as a practicing religion, but as a source of literature and philosophy — and the other his is interested in rugged "Americana," the cowboy/rancher/New Mexico stuff. What unites these two fascinations of his is that they are about as far as you can get from his "born" identity: a wealthy, highly-educated scion of German secular Jewish immigrants on the Upper West Side of Manhattan.

Ray Monk, in what I think is a pretty psychologically perceptive biography of Oppenheimer, talks quite a bit about this. The "cowboy" identity emerged when Oppenheimer was struggling at Harvard as a teenager. These were the years of great discussions of Jewish quotas, and in some ways the most open period of anti-Semitic discussion at the university (previously it had been there, but somewhat "assumed" rather than "asserted"). Oppenheimer had a roommate from New Mexico who embodied everything that Oppenheimer was not: a "true American" who lived near ranches and knew how to "rough it" and who was also a poet and intellectual. Oppenheimer became infatuated with the lifestyle (and maybe a bit with the roommate) and this was Oppenheimer's introduction to the American Southwest and all of its associations. It is easy to see this as an "escape" identity for someone otherwise so under pressure.

The interest with Hinduism sprung up under similarly adverse circumstances, when Oppenheimer was in graduate school in Europe. Oppenheimer went to graduate school very young and struggled immensely at first while he was in England, trying to do experimental physics (which he was awful at). After something like a nervous breakdown, he ended up reinventing himself as a theoretical physicist and going to the Netherlands for study. There he developed the "Oppie" character ("Opje" as they said it) who was wildly clever, confident, and interested in all sorts of Eastern esoterica. Again, this is sort of an invented identity to substitute for his more vulnerable "original" one, and once again you have an interest in something that looks very, very different from anything his father might have advocated. (His father, Julius, was a German textile merchant who was a major supporting of Adler's Ethical Culture, a highly assimilationist secular Judaism that Oppenheimer found to be soulless.)

Anyway. The point here is that this part of Oppenheimer is a very deliberately constructed identity, and I think it is fair to say that this story (which only emerged over a decade later) of Oppenheimer thinking about his own translation of Hindu epics when seeing the first atomic bomb is similarly constructed — not exactly something "off the cuff." It certainly should not be seen as something that would make a lot of sense to others who had not lived through his own idiosyncratic experiences. It is an affecting quote, to be sure, but as noted very few Westerners would know how to read it in context, because the Gita is not a common text here (though it has had its times of greater and lesser interest among Western non-Hindus).