Yes, in key areas. This is the most important question.
- Machu Picchu: You will have a strong 4G signal in the town of Aguas Calientes and at the entrance/main plazas of the Machu Picchu citadel.
- Inca Trail: You will have a signal at the starting point (KM 82) and intermittently on the first day. After that, you will have no signal for most of the trek until you reach the Sun Gate (Inti Punku), where you will get a signal back to post your "I made it!" photo.