Gearset has full support for spinning up and deploying to/from scratch orgs. You can read more about that process in the scratch orgs configuration walkthrough.
Any scratch orgs you create through Gearset will automatically appear on both the Connections page and the Compare and deploy page, listed as scratch orgs.
Adding scratch orgs created outside of Gearset
You can use a scratch org created outside of Gearset, but it's less straightforward, due to Salesforce API limitations:
You would need to create the scratch org and then reset the password. To find out how to do that, click here.
Once that's done, you would need to add it in Gearset as a sandbox org in the Connections page, using a custom domain.
It won't be automatically deleted when it expires, so this has to be done manually.
Accessing scratch orgs created in Gearset, via the CLI
If you've created a scratch org in Gearset, and now need to access it in another tool, such as the Salesforce CLI or Visual Studio Code, then you can do that by resetting the password for the scratch org.