safe USB caharging cable LED mod
This is 100% safe. Using the 5V rail as a voltage source for a parallel 20mA LED won't affect the supply or the cell phone at all. Your diagram does not show any series connection btw.

This is 100% not an activity light. It will always be solid on, barring an weird supply design. It will be on with no cell phone connected, will be on while charging, and on while not charging.