Initially, when looking for information about these modules, I found descriptions that were suggesting the load was separate from the battery, making possible to skip the switch.
Deepening the research, I found another page where, for the same kind of board, it is suggested to disconnect the load when charging.
So, looks like the information I got initially might not be precise enough.
To play safe I believe we always need to include the switch to cut power to the board when charging.
Sorry for the confusion I may have created.
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