Why do you think so? I mean this as a serious question because that's not apparent to me.
If a numeric keyboard makes it easier to enter numbers, and a Japanese keyboard makes it easier to enter Japanese, why shouldn't an appointment keyboard make it easier to enter an appointment time?
I could totally see Apple saying "The custom keyboard is meant for languages and special characters/symbols, not to be used by an app in this fashion"
Wouldn't be the worserejection-reason they've given. You might even find an app that does the same thing already on the AppStore, but that won't stop them from rejecting you because that's just how they roll.
I hope Apple won't get too upset.