Well, I suppose it would follow if it actually achieved anything. If you're willing to blow someone's limbs off and leave him crippled for life to achieve a result, I suppose he has a point that giving them a beating isn't any more horrific a way to achieve the same result.
The problem though is that torture hasn't been showed to achieve anything comparable.
For a start, at least theoretically, a war isn't just about killing people for the sake of killing people. It's for stuff like taking territory or whatever grand goals. Killing or disabling the armed forces preventing you from achieving that goal is one means of doing it, but not the only one, and not even usually the best. E.g., even in WW2, bypassing troop concentrations where possible, or encircling troops and making them surrender, has almost invariably worked better than just assaulting head on and trying to kill as many as possible.
And more than a war was won by just breaking the enemy's domestic support for that war. E.g., that's how North Vietnam won that war.
But really, one just needs to read Sun Tzu. Just killing as many enemies as one can is almost always the wrong way to go about a war, and never a goal by itself.
Which gets us to torture. Sure, if torturing someone would get a Saddam or Osama Bin Laden to surrender, I could see Sam Harris's point. It would be another mean to the same goal.
But the problem is that torture almost never achieves anything. It doesn't produce reliable information, it doesn't cause the rest of the enemies to surrender, etc.
In fact, if one reads Sun Tzu, it's hard not to notice one thing: soldiers will fight harder if they think retreat or surrender are not an option. He even advises to place one's troops on "death ground" deliberately, when you want to get the most out of them.
Having such a reputation that surrendering to you is a horrible option, just transforms a lot of tactical and operative situations into "death ground". If people can't safely retreat, and would rather die than get tortured horribly by you, they'll fight instead of surrendering.
And that's just one aspect for why that's a bad idea.
Domestic support for the war -- even just guerilla war, if they can't oppose you head on -- is also likely to be higher if you basically make yourself a monster to be stopped at all cost. It's something Germany discovered the hard way in Russia in WW2, for example. You can't break the will to fight early and win the war, as Sun Tzu advises, and you're setting yourself up for a long war, which, as he notes, is almost never a good idea.
Local support for YOU, which, again, is one thing Sun Tzu was advising to get if possible, as it can make your job much easier and cheaper, is also going to be almost nil if you have the reputation of a monster.
Etc.
Really, there are good reasons to be smarter than that in war.