I can't imagine they designed it to send notifications many hours later or not at all.
But as long as you constantly check it, it can get the job done.
The only downside to waiting is risking that the price increase of a cruise could negate NextCruise perks.
But a week shouldn't be risky. Just pay attention to the RC website (you can access the RC website without any Voom package) so you know the going rate of the cruise since they can have "sales" that increase the price at times.
I've seen people get busted for putting vodka in water bottles.
So yes, they check. Granted I bet more gets through than doesn't, but they are looking.