Does the word addict come from Greek allos?

No, the word "addict" does not come from the Greek word "allos" (ἄλλος), meaning "other" or "another".

The word "addict" comes from the Latin word "addictus," which originally meant "one who is given over or devoted to something," often in a legal context referring to someone bound over to a creditor or court. The modern sense of being enslaved to a substance or habit developed later.