not yet, but we're currently working on it, hence - your browser asking you if you'd like to allow Todoist storing data in your computer.
New browsers support the HTML 5 offline mode and that's what we're implementing into Todoist right now. This will indeed allow Todoist to be used completely offline with the data stored locally on your computer.
You can get more detailed info about offline web applications and HTML 5 here:
Thank you for the quick reply, the status report, and the link. I use Prism to have a desktop experience with Todoist - it's convenient to have Todoist on my Toolbar (Windows) - however, it's not really offline. Having a true offline function for Todoist is exciting! Wonderful work, great support!