Is it possible to add a person to watch an exising issue, without assigning the task to him/her?
Absolutely, this is documented within Watching and Voting on an Issue:
If you have the correct permissions (see below), you can also
view the voter and watcher lists for an issue and, you can manage the
watcher list — that is, add other people to the watcher list. This is
useful if you need to draw someone's attention to a particular issue. [emphasis mine]
The relevant permission is:
- Manage Watcher List — permits a user to view/edit the watcher list.
You can manage the list by clicking on the watcher count icon:
