Significance of the alcoholic housemate

The housemate you reference is actually Bennett's father. This review from Emanuel Levy explains the significance of the relationship and also points out that there are 5 father-son relationships in the film:

I don't know if Gaghan subscribes to Freudian psychology, but one of the unifying structural elements of “Syriana” is intergenerational conflict, manifest in the troubled relationships between fathers and sons. There are no less than five sets of fathers and sons in the film...

Bennett Holiday and Bennett Holiday Sr. (Jeffrey Wright and William Charles Mitchell). Bennett is an ambitious Washington attorney at Sloan Whiting law firm, in charge of the task of guiding the Connex-Killen merger. It's in the company and the country's interest that the merger goes through. It also serves his personal ambitions. Bennett's upward mobility is complicated by his difficult relationship with his father, an alcoholic who faults his son for working for the establishment. While he has always denounced his father as a failure, as Bennett is drawn deeper into the morally ambiguous world of the industry, he starts to doubt his own right to judge his father's character.

Gaghan was the writer and director of the film. The other father-son pairings were Bob and Robby Barnes (Bob worries about losing his son as he goes off to college), Bryan Woodman and his two young sons (one drowns in the pool), Emir Hamad Al-Subaai and his two sons, Prince Nasir and Prince Meshal (the older son is in line for the throne, but is too reform-minded), and Saleem Ahmed Khan and Wasim Ahmed Khan (migrant workers who dream of returning to Pakistan).