Ok, you're right. In this example, "Eier abholen" would mean I've ordered them previously; "Eier holen", not necessarily so (if preordered, most people would rather say "ich gehe morgen die Eier holen", though this is only a usage and not a rule).
On the other hand, if I'm ordering eggs or something else, there's no difference whether the merchant asks me "Holen Sie's, oder soll ich's liefern?" or "Holen Sie's ab, oder...?"