It could work. In fact, I might try wearing duct-tape armor to see how comftorable (I know I misspelled that) it is. Comfort is one of the most important parts of armor--otherwise you'll get distracted and irritated, making the armor useless in close combat.
I doubt that most people have enough duct tape on hand to make a good suit of armor. I would wear a strong but relatively light material (denim and leather being good choices, as they both qualify and are common [try ripping through either with your teeth. It's not easy, so they could stop at least a bite]) and reinforce some areas with duct tape (elbows, knees, wrists, ankles, waist and any other area where there is a gap in the clothing and/or is likely to wear out quicker). It would also be a good idea to carry a roll(s) of duct tape, because if you can't fix it with duct tape, it ain't getting fixed (at least not in the chaos of the initial stages of the zombie apocalypse) and you can use it for a wider variety of things than anything else you're likely to find lying around the average house.
Yes, you would look incredibly cool. However, coolness will not keep you alive in the zombie apocalypse. Besides, you have clothing to use as clothing, so don't waste the amazing resource that is duct tape to make clothes.