My opinion:
Yes it will work but it will be very inefficient and the battery will never properly charge to full capacity. What you are proposing is to connect a lead acid charger to a cell balancing circuit then to individual Li-ion cells. The charging voltage and current will be wrong, that doesn't mean it won't store charge, it means it may never reach a fully charged state.
The board in the Ebay link is not a charger, it is a load balancer. The idea is it limits the voltage across each cell individually so that if they are at different states of charge or if one or more fails, it doesn't cause a cascade failure of all the others. You can achieve almost the same effect by wiring a Zener diode across each cell but doing it that way would cost more.
You have never described exactly what you need. I think what you are asking for is a circuit that takes power from a PV panel and converts it to a stable 12V output for your equipment and diverts any surplus power to a battery. When the PV is unavailable, the battery provides the 12V output instead. Am I correct?
Brian.