No. The author assumes that it implies that. For the user though, it can imply many things:
- Something loading in the area next to the text, indicating something's coming up to that region soon, and when it disappears, it might be interpreted as a loading error.
- UI is doing something, so not responsive anymore.
- UI is doing something, and if the user does something, they might disrupt that process.
- Internet connection is slow.
In general, a loading indicator that starts running when a checkbox is selected is bad UX.
Better UX alterntives would be:
- Directly animate the checkbox itself when clicked (like pulsating it, or the checkbox square starting to rotate in a pattern, etc), and show a stationary checkbox when the operation is complete.
- Don't show user anything at all, let the checkbox show that it's been checked right away. If the user wants to leave before it's processed, just warn them about unsaved changes. (FastMail does that, for example)
- Don't use checkboxes for asynchronous UI actions that can take time. Use buttons instead, so the user understands the UX language. Then, you can use loading animations as much as you want.