Cold Brewing coffee - does it use more beans?
Obviously, this will depend on your personal preferences and how you brew the coffee.

The canonical measurement is about 2 tablespoons of coffee per 6 ounce cup, or about 2 3/4 cups of ground coffee per gallon of water.

Typical ratios for cold brew coffee, such as suggested Chow are 1.75 cups of coffee to 3 1/2 cups of water for the concentrate, which would then be diluted by a like amount of water for drinking.  That is a ratio of 1.75 cups of coffee to 7 cups of water, or about 3 3/4 cups of coffee per gallon of water (I am generously assuming the ratio is based on measuring cups, not "coffee" cups).

So the cold brewing method uses about 1.35 times more beans than the traditional methods.

You will have to decide if you prefer the flavor of the cold brewed coffee enough to justify the increased amount of beans required.

As to whether you can produce enough, that depends on what equipment you have, how much trouble you are willing to go to, and how much storage space you have.  There is nothing about cold brewed coffee that would prevent you from producing the concentrate in large quantities.  At the volume you specify (assuming you mean a 6 ounce "coffee" cup, and it is three cups between the two of you), you would need about 45 ounces of concentrate for a week, which is about 1.5 quarts (or liters).

See also:

Bottling and Storing Cold-Brewed Coffee?

Concentrate should easily last you throughout a week, if you have room to store it.