Thanks for asking these questions. It may help improve all of our knowledge.
My take, which may be incorrect.
The actual adjustment range on a power supply is often greater than the quarantined range to allow for manufacturing variance.
Neglecting any voltage drop in the connection leads, the voltage on the battery and the output studs of the power supply will be the same. Basic electric theory sStates they cannot be different. Provided you are not exceeding the output capacity of the power supply, and you don't want to release smoke by doing this, the load and no-good voltage must be within the regulation tolerance of 2%.
As the battery charges the current from the power supply will decrease. This is one way you can determine charge rate. Voltage will not be a good indicator on its own.
All this presumes the SP200 is an adjustable, regulated power supply without a charge controller. If I read the spec incorrectly, my comments aren't worth the time to read them.
I assume it would be used by monitoring charging current and voltage. Adjust the output voltage to give the correct value for stage 1,2 or 3,without exceeding the output current of the power supply. Commercially, the voltage is set at a higher voltage periodically to equalize the cells.
Curious what good values would be.