Hi @wizard,
Welcome to the community!
Yes, it is possible, even though click events are not really part of the DataTable component.
Please take a look on this old post that is pretty much related to what you want to do. The only difference is that you need to use as Output the data property of dash_table.DataTable. The data format in active_cell is explained in the DataTable reference.
As a second alternative, you can look into this recent post. It uses an additional library (dash-extensions), however it is arguably a better UX to use a double click to change the data.