Should users be given an option to turn off the confirmations across the whole website? An example could be to add a checkbox under user settings that turns the confirmations on and off for actions like leave an unsaved page, delete a record, etc.
If you don't provide the user the possibility to turn off a single confirmation, it looks to me like a bad idea as it will probably be used to turn off a single useless or annoying confirmation without being able to evaluate the whole impact of this action.
A better design may be to add a "Don't display this confirmation again" checkbox to each confirmation (or each non-critical confirmations) and save this setting per user.
Confirmations are an important part of a user interface. They make sure that the state of the application is clear to a user. That said, you don't have to slap them in the face with these confirmations.
When designing your notifications you need check if each confirmation is actually necessary. Perhaps the application state is already obvious through other means. E.g. a deleted record might be removed from the screen or presented differently (strike-through), so that other confirmation is not required.
You could also provide a second, suppressed level of confirmation. Use subtle indicators for common confirmations or confirmations users have already seen.
If your confirmations are well-designed, there should be no reason for users to configure their behavior. Users should focus on accomplishing their tasks, and should not have to worry about configuring an application's behavior: that should be awesome, useful and friendly right out of the box.