I suggest making friends with a police officer and asking him/her that very question, because every situation is different, as is the law from state to state.
For example, in your scenario, if X and Y are laughing and joking around and the police think that the call they got was a deliberate false report, someone might get arrested. But if the officers on the scene don't think that X and Y are involved in anything potentially violent (after questioning them thoroughly), and that they didn't participate in making a false emergency call (which is against the law everywhere in the US), probably nothing would happen.
The third scenario that occurs to me is that the police would question X and Y and try to find out if there is a possibility of trouble. If this were a domestic violence call, for example, they would probably try to be sure that neither person was in immediate danger. If they believed that one or both persons was in real danger, they'd take some kind of action. Of course, the presence of children changes things, as would the presence of other adults.
But if X runs away as the cops drive up, X is going to be pursued and questioned, at the very least. Arrest would be a definite possibility here.
Sorry, but other than the running away part, there isn't an absolute yes/no answer to this question. It just depends.
