In my mod I'm wanting to make several days pass by in an instant. I was considering trying to simply set "GameDaysPassed" to the current value + the number of days, but I'm not even sure that will work as intended.

What do the wait/sleep/fast travel functions use? Do they work in this exact way? Is this a valid method of doing this?

You could change the 'timeScale' to a high number and check for the current day, then then set it back to what it was.
Or you could change the day but you would also have to change the month if you are at the end of the month. (i suspect)
GameDay
GameMonth
Both are global variables that you can import into your script as properties.

Interesting. I knew about timescale but I didn't really understand what it was for. How exactly does it work? I've seen it referenced in a few scripts but I don't really know how to determine how much game speed is affected by it.

Its how fast ingame time passes compared to real time.

The value it contains is the number Minutes that pass in-game within one minute of real-time.

So if its set to 1440, a day would go by in 1 minute. (60*24)
If my math is right, 86400 would have a day pass in one second.