Yes! You can always save what you have started and we'll keep it in your account until you're ready to send. You will need an account in order to save your invitation or card.
If you are designing an invitation, the first step would be to click the "Save and continue" button to save the design (don't worry, you'll be able to change it before sending).
After you leave the design editor the invitation will be saved in your account. If you are not signed in, click the "Save for later" button on the following page.
When using the Punchbowl app, your invitation will automatically be saved to your account when you hit the "Finish Editing" button that navigates from the design portion of the invite to the add guests section.