Can the new
operator throw an exception in real life?
And if so, do I have any options for handling such an exception apart from killing my application?
Yes, new can and will throw.
Since you are asking about 'real' programs: I've worked on various shrink-wrapped commercial software applications for over 20 years. 'Real' programs with millions of users. That you can go and buy off the shelf today. Yes, new can throw.
There are various ways to handle this.
First, write your own new_handler (this is called before new gives up and throws - see set_new_handler() function). When your new_handler is called, see if you can free some things you don't really need. Also warn the user that they are running low on memory. (yes, it can be hard to warn the user about anything if you are really low).
One thing is to have pre-allocated, at the start of your program some 'extra' memory. When you run out of memory, use this extra memory to help save a copy of the user's document to disk. Then warn, and maybe exit gracefully.
Etc. This is just a overview, obviously there is more to it.
Handling low memory is not easy.