Is it possible to visualize the CellID in notebooks?

I am interested in using the CellID, but I would need to be able to see it (without doing Ctrl-E..)

Is it possible to automatically set the CellLabel or the Tags to the value of the CellID? I have been trying for a while, but no luck.

I want to be able to do this for a new style BTW.

Is there code run when a cell is created or deleted that is setable by the style?

The answer is “no” to both questions.