In theory yes, but buying an iPhone in one country to use in another country can have many problems:
LTE Find the right iPhone for the right country or region. - http://www.apple.com/iphone/LTE/
E.g., Using American iPhone 5 in Europe - https://discussions.apple.com/thread/4593901 - Yes, but no LTE support.
Some carriers will not accept unlocked phones - https://discussions.apple.com/message/20359060#20359060 - E.g., "Virgin Mobile, like all CDMA carriers, will only activate devices on their network that were initially sold for use on their network." and https://discussions.apple.com/message/33206605#message33206605 "The iPhone 7 and 7 Plus sold unlocked and for use on AT&T and T-Mobile is not physically compatible with the Verizon and Sprint networks."
Other issues - https://discussions.apple.com/message/33176952#message33176952 - "The Japanese carriers are notoriously difficult to work with when it comes to unlocking. If you are not a customer of the carrier it's locked to, they will not unlock it."
Warranty restriction! - http://www.apple.com/legal/warranty/products/ios-warranty-document-us.html - "IMPORTANT RESTRICTION FOR iPHONE, iPAD AND APPLE TV SERVICE. Apple may restrict warranty service for iPhone, iPad and Apple TV to the country where Apple or its Authorized Distributors originally sold the device." <-- The warranty does not outright deny warranty coverage in other countries but there are many limitations to the effect they almost certainly will refuse to do repairs under warranty or even repairs at all except where you bought it. The phone would have to be sent to a friend in the country of purchase to handle any repair claims because Apple will not handle international shipping. Even if you are willing to pay for repairs yourself it is likely Apple will not repair it in another country.
New phones may also have tax added to the cost (e.g., in the USA prices do not include taxes), and you may have to pay import duty when bringing an expensive phone into your country.
