No other country has intelligence services with even a fraction of the reach of the NSA, so clearly countries can exist without an NSA class agency.
Whether a country could exist without an organization that pays attention to what the rest of the world is up to is another matter. It's a role served by diplomatic services, and where even the most low tech intelligence agency can provide substantial additional abilities without stepping all over civil liberties. I don't see anyone questioning the need for a diplomatic corps, foreign service, or even basic human intelligence agencies, or for that matter basic sigint.
But it's an entirely different issue than whether an agency like the NSA is needed - or warranted.
Arguably, while the NSA may thwart some threats, it is also part of maintaining the image of the US as the big bully of the world, and as a result it is part of creating the type of threats it is meant to protect you against. It's self-reinforcing.