Actually, "potentiate" means "to increase the effects of" - and falling asleep isn't an opiate's #1 goal. Thus, DPH isn't actually potentiating the opiate, just potentiating the nod.
Promethazine does the same. They both however have anticholinergic effects and cause delirium at higher-than-recommended doses.
Codeine is much weaker than Hydrocodone. The syrup probably has an unfavorable ratio of codeine to promethazine for it to be recreational in itself, but adding it to the base hydrocodone with intensify effects of all compounds (aside from the promethazine-induced delirium if you reach that point).