According to 2011 Moderator Election - Town Hall Chat Digest, the answer is yes. And here I thought my memory was going! But still, making gratuitous changes is rather childish, and forces me to delete the comment entirely (if I notice it).
Not relevant here, but I note in that chat I was working on the assumption that moderators would 'turn over' with regular elections, as in politics, rather than the situation we actually have where moderators continue indefinitely and elections are only for new people.– Joseph Wright ModJun 30, 2016 at 16:34
@JosephWright - The reference was simply the first useful one my search found.– John KormyloJul 1, 2016 at 0:04
It's not childish if the comment in question (pun not intended) has some problems that require moderator intervention while still having useful info. Other situations require minor edits, but it's usually done in accordance with site policy and with being "janitors".– AlenannoJul 8, 2016 at 12:01
Yes it is possible for moderators to edit comments. In practice this is normally done only if the commenter requests it (as they've spotted an error but have missed the editing window) or where there is a typo that is clear and correctable. (Both cases are rare so I can't readily point to an example, though I know I've corrected things for people on occasion; I normally let them know this has been done.) Far more common is simply deleting comments, for example ones that are no longer relevant (e.g. 'Please add a MWE' after this has happened).
Yes, moderators can edit comments. The other answer lists a few cases in which this is done.
As a moderator on another site, I've also edited comments to remove rude/offensive content if the same comment also contains useful information (e.g. in a debate in the comments). Similarly, comments can be edited to remove personal information (such as an e-mail address) while keeping useful information.