Yes, the word "away" is being omitted here. In general (it's hard to explain specifically), the omission of the word "away" removes partially the sense of physical distance between the speaker and the object, and makes it more of a metaphorical distance (although also somewhat of a physical one). In this particular context, the object of the "keeping" is God, who is not actually a physical thing, and so the notion of a physical distance between the speaker and God is somewhat nonsensical, hence the meaning is more of a spiritual distance (in context) [^1].
As for general usage, I would say that the word "away" should always be included when one is talking about physical distance (e.g. "I want my stalker to keep away from me", or "I'm going to keep this ball away from the other team"). When talking about metaphorical distance, the word "away" can be included or not (e.g. "nothing can keep you from me" is a phrase usually used by someone in love, where the distance is both a physical one, but also a metaphorical one in terms of sending one's loving feelings to another; the phrase "nothing can keep you away from me" has a similar meaning in context but is much more referring to the physical than the emotional distance).
There is, of course, the third meaning raised in the comments which is where "to keep" takes the meaning of the verb "to prevent", e.g. "I don't want to keep you from your work" ("I don't want to prevent you from doing your work"). In this context, "away" can also be included ("I don't want to keep you away from your work"), but it is not common to do so, because the physical distance aspect is not as great (the latter has more of a meaning of the person being physically separated from their work and being prevented from going back to doing it, while the latter means more that the person is preoccupied with something else, even though they may physically be at their desk, which is the more common usage of that phrase). The phrase, for example, "the goalie keeps the opposing team from scoring a goal", would not make sense with "away" included, as the meaning of "keep" in this phrase is 100% "to prevent" and has no relation whatsoever to distance.
[^1]: With relation to God in particular, religious people often equate the spiritual difference between oneself and God with a physical one, and so, in the context of specifically God, one can include "away" even though the context is not physical at all.
(I don't know how to do footnotes on this thing, hopefully my formatting works, if anyone wants to edit this answer and create a proper footnote it would be appreciated)