No, not necessarily. And I'm not sure that a category such as "recipient" is in play at all. By placing these nouns in apposition to the understood subject of the verb, he is describing the Son in terms of these nouns.Of course, that is the most basic generic definition. You are probably aware that ἀπαύγασμα can be active or passive.
Does this mean that the Son as the recipient of the χαρακτὴρ of the Father (cp εικόν Col. 1) is coordinated with the Son as the recipient of ἀπαύγασμα?