This may depend on sanctioning body then. We have rarely played games that have safety bags but I have seen twice where the batter was called safe because the first baseman did not touch the actual base but did touch the safety base. I did not see anywhere in the rule book that stated if the ball is thrown from foul territory that the baseman can occupy the safety base but that may be the case. All I could actually find on the subject was that the safety bag is for the batter only and once/if the batter becomes a runner then the safety base no longer exists. This is just my experience with the matter.
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Outside of maybe Little League which I have no idea, the other orgs we have played allow it on throws from foul territory.