Yeah, but "daimon" could also mean "soul", als in "eudaimonia" or "daimonion" (Sokrates' word for "conscience"). My Greek teacher explained to us that the "basic meaning" connecting all those different meanings was something like "supernatural force or entities that influences men". This also applied to lesser deities or supernatural beings (the major gods were usually called theoi) like demons etc. That was the reason it was applied to the christian concept of demons, since they also could influence men through possessing them.
However, you state of course correctly, that "daimon" would not really have the same connotation as our christian influenced understanding of "demon".
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