The short answer is no. For Segment Pro (SP) you are going to have to go to Share / export. A .json file should be placed in your user/document/my segment pro folder. Then transfer the json file to your new computer and use the Share / import.
The older software WoodTurner Pro creates a wtp file that is a stand alone and can be moved without the export/import process.
It is not a bad idea to export some of your finished designs in SP and create a json file. Save them to a thumb drive for safe keeping. Same goes for WTP files. Always good to have a back up.