Do batteries in series equalize charge
Not generally a good idea, but it depends on the battery type.

NiCd is very tolerant of overcharging, and will equalise ok if you keep the current below C/10.

Other technologies will not work. Lithium batteries even have separate 'equalising wires" connected to each cell, so the charger can adjust the current individually.

Worse than charging an unbalanced pack is discharging it. The empty cells will be forcibly drained far past their safe minimum voltage, possibly until they are inverted. This will cause permanent damage, even if done at low current.