The answer is... it depends.
Using non-public API is not permitted, and these Darwin notifications are not publicly documented. So the official answer is no, you are not allowed to use this notification in a production code. Otherwise, you risk getting this unpleasant email from Apple:
Your app uses or references the following non-public APIs:
com.apple.springboard.lockcomplete
On the other hand, I've used that very notification for 4 years till I got a rejection from the App Store for one of my apps. Another app of mine still uses it without problems. So if you really need it and you think it's worth the risk, you may give it a try.