As the battery becomes fully charged, the current will taper down to a value which overcomes the small losses in the float condition and the inverter standby load if turned on. If a load is introduced to the inverter the array will divert current to the inverter, as long as the load current dose not exceed the array output, the battery will remain in its fully charged state. If however the load is greater than the array output, the battery will make up the difference thereby discharging in the amount of the deficit the array cannot support.
Using the otherwise wasted power is what is referred to as opportunity loads, such as using a washing machine when the battery is fully charged and there is still sun available.
Care must be taken to ensure the loads don’t exceed the arrays ability by too great a margin, each system is different so getting to know what your system can supply is of paramount importance, watching the battery voltage during such loads can give an indication, if the voltage begins to drop, then the battery is being discharged. If you have a clamp on ammeter the current from the array and the load current can be measured to ensure they are close.
Passing clouds will sometimes draw current from the battery but if the arrays output is sufficiently sized it will replenish what was taken out, one has to study the system over time to learn it’s limitations and maintain a ballance.