Depends on how your e-mail is configured. How do you access your e-mail on your laptop? Using a webmail interface in a browser? Then the answer is no, unless you use onboard WiFi. Using a standalone e-mail program such as Thunderbird, Outlook, Apple Mail? Then yes, provided the program is configured to store the messages on the laptop itself. If that is not the case, you'll need to use the WiFi again.
You can figure this out yourself, just switch off the WiFi on the laptop and see how you get on.