You are right, Sorrow, about the nature of spiral climb from the pursued plane perspective.
However, the chaser does not fly the longer path. Neither does it have to climb faster, at least not in initial phase. Smart follower can negate spiral climb very long too.
Spiral climb capitalizes on opponents greed and his try to do a lead turn from pure pursuit.
It works best in good climbers, but it can work in any other plane, depending on the initial situation.
For example, you are in good climber, followed by a poorer climber. One of the options is the spiral climb (surely not the safest one).
The first thing I'd do is to bleed speed to best sustained climb speed for my plane. Now I slowly start right hand climb (since left hand torque will make it harder for the pursuer). I bank just a little, add rudder to negate the side slip and wait, watching the opponent reaction.
At first, opponent will gain because he will cut corner. Smarter opponents will beat spiral climb by choosing the flight path way in front of you, at point where your spiral will take you later. They climb with no banking and can be even more effective against your climb. A snapshot can ruin your day. Even if they miss, the can Immelmann and lead turn your spiral again.
However, the opponent who goes for dead 6 approach in spiral climb is likely to get himself rope-a-doped. At one point he will have to bank more than you and his AoA will also have to be higher. There goes his sustained climb, he will have to nose down to pick up speed and come again. It is important that you don't make the same mistake, always climb at best sustained climb speed and never lose it.
Little by little you can gain angles and alt this way. Once started, spiral climb can rarely be stopped. When you see the opponent at your 3-9 line and lower, you know you are getting on offensive now. Now it is question of timing. Usually it ends in nose high turn and hammerhead/wingover at low and slow enemy.
However, I think Daniko used expression spiral climb as a figure of speech, rather than he ment this particular technique is advisable against multiple opponents.
Spiral climb is not an easy technique and it is almost impossible to do against multiple enemies.