how the battery behaves in this diagram
how a battery behaves in parallel to the charger with a shared load but with a voltage difference
My Xtal ball says you are thinking of this;
51V (58.8V) 5A Li-ion / LiFePO4 Charger Works with 14S Li-ion batteries and 16S LiFePO4 batteries.
When you put a load on the battery while charging it defeats the cut-off detected by the current in CV mode dropping below 5% ( or so) . Failing to do this can significantly reduce battery life by the amount of time spent in CV mode.
Otherwise, in CC mode, no problem since your charger will share CC (5A) between battery and load current, so it takes longer. ( just like your mobile)
But if in CV mode, you must limit the time spent charging at 58.8V if the system does not monitor Battery current separate from the load. ( read up at Battery University site)
The charger seems to be limited to 5A, so if the load+battery tries to draw more than that, the charger will reduce its output voltage to a lower value until no more than 5A are drawn from the charger.
As long as the charger's voltage is higher than the battery's voltage, current will flow into the battery and charge it. If the load draws 5A or more, the charger's voltage will drop and finally reach the battery's voltage and any extra current draw beyond the 5A will be sourced from the battery.
If you're wondering if the setup will work:
Yes, it can work as desired, if the charger is not too smart and can handle extended periods of maximum output current.
A "smart" charger may detect that something seems to be wrong with the battery because it seems to draw much more current/accept much more mAh than it should. The most simple safety mechanism that could get into your way is just a safety timer in the charger set to turn off after a certain time after which the battery should definitely be fully charged. Notice that in your circuit the battery will never be charged but in fact be discharged although the charger is connected, which may trigger a couple of different safety mechanisms in the charger.