This overlaps a bit with what rjenkinsgb has just said, but I started writing it before he posted.
An 18650 cell can be 3000 mAh or more. The 66 mA would balance a completely imbalanced set in around 50 hours.
However, cells going out of balance is something that takes time as well, so if you balance a series set first, a small balancing circuit is probably all that's needed. Really good quality batteries have balancing systems, and they are only capable of very slow balancing rates. All the balancing circuits that I have seen are resistor banks within the battery, and they are not sized to get rid of a lot of power. However, the cells are guaranteed to be very similar, and the battery management circuit can detect an imbalance and turn on the balancing at any state of charge.
On the simple circuit you have, the balancing will only happen during the charging, and then only when one cell gets fully charged.
The balancing does rely on the charging system limiting the battery voltage near the voltage of the balancing circuit. If the charging circuit cuts out as soon as a cell reaches 4.2 V, the balancing won't really work.
Say you have two cells in series, and one is at 3.9 V and one at 3.7 V. Fast charge will result in the voltage rising quite quickly, and soon the cells will be at 4.2 V and 4 V. At that point the balancing board will start to bypass 66 mA from the cell at 4.2 V. If the charging circuit holds the largest cell voltage at 4.2 V, then the lower voltage cell will be charged at 66 mA more than the high voltage cell, and eventually the lower voltage cell will rise to 4.2 V as well, and balancing is complete.
However, if the charging circuit keeps supplying a high current, much more than 66 mA, until the battery is at 2 * 4.2 V, the higher voltage cell will be overcharged, and may be damaged before the total voltage is 8.4 V which will be when the current drops. When that happens, the 66 mA will eventually bring the higher voltage battery down, but it's not a good way to treat the cells.
Also, if your charger prevents the cells from ever getting to 4.2 V, or cuts out completely as soon as one does, then there will never be any time when the balancing is working,
So, as usual, the devil is in the detail. That was why I said before that the balancing circuit "would probably work". If you do use it, monitor it carefully during a charge cycle and make sure that it is doing what you want. Write down times and all the cell voltages and prepare for a boring couple of hours.