You can stay on induction for longer than the two weeks, but there are a few things to consider. First...many people find that they actually lose better when they increase their carbs a bit. Second...what will you do if you hit a stall or plateau? Drop to 15 grams of carb? 10? If you stay at 20 grams for a long period of time, you won't have anywhere to retreat to if you hit a stall.
Having said that, Dr. Atkins does say that you can safely stay on induction for longer than the two weeks (safely meaning that it won't cause you any physical harm), especially if you have a great deal of weight to lose but the point of low carbing is to not only lose the weight but to also learn how to keep it off for a lifetime. If you stay at induction levels until you get to your goal or close to your goal, you really won't have any idea how you should be eating to keep the weight off.
Ongoing weight loss (OWL) is where you practice and tinker and tweak until you figure out what your maxiumum level of carbs for losing is. Once you figure that out, you'll also have a pretty good idea what your maximum level of carbs for maintaining will be too. You also get the benefit of greater variety.
It's an individual decision, but if it were me I wouldn't stay on induction too much past the required 2 weeks.