I don't know, if I found a plate of spaghetti with a nice note telling me the kind spaghetti-giver will come get me shortly - someone who offers food, shelter, protection, and entertainment - what’s not to like? - I’d wait for them. And hey, even if you don’t like word puzzles, there's still paper and crayons to doodle with. Sure, I'd go looking if no one came and I got hungry again, but Sans would probably check in the meantime (cuz Papyrus would keep asking) and he can "shortcut" to and from instantly. If the royal guard went by, Frisk would just deal with them sooner rather than later. But they're not likely to - they've got their own stations to man, and the only one stationed further out than Papyrus is Sans.