most likely. that is why jiraiya is with him most of the time.
i guess when hes by himself he is at a greater risk but i guess she is willing to take that chance. she nows naruto and she nows that he won't betray the leaf. she also knows that itachi and the atkatsuki want him alive (could have limbs chopped off as longs as he is alive). they want kyuubi and they need naruto breathing for that.