Your question is a bit all over the map but, ultimately, it's about tone.
Your silly example would be fine for a first person narrator who loves puns and can never be completely serious. If it's the only time s/he ever said anything like that, it would be very out of place and jarring.
If your example is a character's dialogue, then it depends on the character. Pretty much anyone hearing that line from someone in real life would roll their eyes (and maybe cross the person off their next invite list), unless they were into the absurd.
It's just not a line someone would say about their breakup. The only way it works is if it's two characters (preferably teens or younger) playing amateur detective who enter a location and decide to split up to cover more ground. Even then, it's odd.
If the tone of your book isn't consistent, it will annoy your reader. Sure, it's okay to have sad parts, joyous parts, and so on, that's not the same thing. But if you throw in every idea you have, it's going to be a mess.
When you get an idea, write it down! Have an idea journal, or the computer equivalent. But when it comes to your book, cut ruthlessly. Leave what works. Kick to the curb (back to the idea journal) whatever doesn't.