No, once you have installed the desktop version of SoftChalk, you can work on your lessons regardless of whether you are connected to the internet.
If you ARE connected to the internet, when you first start SoftChalk, it will check to see if there are any updates to the software and will download and install those if available. However, if you are NOT connected to the internet, SoftChalk will simply skip the update check.
If you are on the web-based version of SoftChalk Create, available with a subscription to SoftChalk Cloud, then you will need internet access to create content.