The game will cut after sealing the Dark Fountain in Chapter 2
It would seem like that bringing Kris to the hospital room would cause some sort of a paradox, so the voice would cut the connection to prevent it from occurring. Rudy and Noelle will play Undertale after finishing Chapter 2.
Because how would the story continue after C2?- Axquirix confirmed that he'll do Undertale eventually, though hasn't made it clear when it will take place.
Another character will get dragged into the mix in later chapters
Noelle starts playing just as one of her friends come in, and it's too late for them to turn back, forcing them to join the playthrough.