Global Entry is a "Trusted Traveler" program that requires a background check and a yearly fee. If you have Global Entry it greatly speeds up your customs experience, but you still have to fill out the re-entry questionnaire. Since Mobile Passport expedites the questionnaire portion, it would complement Global Entry well, making your customs transit that much faster.
The Mobile Passport app is available for use by U.S. citizens with valid passports and Canadian citizens with valid Canadian passports and B1 or B2 visa status. It is only applicable for re-entry into the United States.
Yes, Mobile Passport requires a Wi-Fi connection to be fully functional. You will be able to enter passport information and answer the Customs and Border Protection questions while offline, but you will need Wi-Fi to submit them. After your plane lands you can use its Wi-Fi if available, or wait to use the airport's Wi-Fi so you can get your QR code receipt before you reach the customs area.