Holy crap, there's a lot to deal with here. First and foremost, a katana will work. I own one. Get out of the mindset that you will be hacking away like a movie. The first strike with a katana is usually a forward, straight strike. Think of a lunge that extends the arms. The people who created this martial art, as I understand it, aimed for the adam's apple. If it connects, lights out. I have a katana. It would not be my first choice.
Not to nitpick, but I disagree with this. I'm not sure which martial art you are speaking about, but a few things:
First, not all people on the battlefield had katana. More to the point, most of the people on the battlefield were not samurai at all, they were common foot soldiers. The majority of soldiers on the battlefield never had katanas, they had yari (long spears), bisento, naginata (for women), bows/arrows, staves and guns - depending on what time period we're speaking about. I'm not saying there weren't any swords, but they weren't nearly as prevalent as you think.
Swords, especially good swords, were reserved for higher ranking samurai and generals, not foot soldiers. That said, most samurai were also on horseback and wore full armor. The Adam's Apple was not a prime target given the armor, being on a horse, and the dynamics of a battlefield. In addition, samurai generally did not gallop into the middle of a battle; they waited until the foot soldiers fought their wars of attrition and then went in to try and kill the enemy's generals.
Simply put, the target was wherever a target was available. If that meant the top of the head, it was the top of the head. If that meant the legs or under the arm, that was the target.
Another misconception that needs to be cleared up is that not all swords were the beautifully crafted pieces we have come to know and love. It was a period of war, and daimyo (feudal warlords) didn't have the luxury of commissioning one or two master craftsmen to create thousands of swords. Most of the swords - especially for those foot soldiers who were given one - were hacking and slashing implements, not refined watermelon cutters. They were trained to hack away at anything and everything in their path, not engage in Musahi-worthy beachfront fight scenes.
Lastly, let's remember that most samurai were just kids and young adults. It was extremely rare for samurai to be 50-year old seasoned fighters with hundreds of hand-to-hand combat kills to their name. Though I don't know the specific number, the average age of soldiers during this period was much closer to 19 than 40.
I don't mean to pick on you, I just want to illustrate some of the misconceptions.
Now, back to our modern reality. Yes, katana are effective weapons. However, unless you are buying a several thousand dollar sword that has a blade specifically created to hold a good edge, you will not be able to sharpen the blade of a cheap katana to hold a good edge; it will chip or break before you get it to be as sharp as a quality blade. You, just like the average Japanese foot soldier, will be hacking and slashing and not precision thrusting. Also, the materials of the tsuka are to be considered. Many factory-made katana can not withstand being used regularly and with full force. The blade will fly out of the tsuka in many shoddy products.
Which brings me to my last point, hopefully not interpreted as hostile because it's not intended to be so:
How many of you/us have actually PRACTICED using a sword against an opponent? Not just a guy who will stand there for you while you aim, but an engaged threat? I mean a moving enemy with his own weapon who is trying to attack you or someone you love. I have, every week for years and years and years and years. Let me tell you something, it's ridiculously difficult... almost prohibitively so. The only way you are going to tsuki (thrust) a sword and hit an attacker's Adam's Apple effectively during a home invasion defense scenario is if you get really, REALLY lucky. Sorry, but it's just not going to happen in my experience.
Does that mean a sword isn't a viable home defense option? Not at all, but you may want to consider alternative methods of its use rather than assuming a perfect thrust is going to work. Chances are it won't.
I realize I'm making the assumption of samurai; regardless, I think if nothing else some historical background will provide good food for thought.