Unfortunately, as of right now, that’s not supported. However, depending on your use case, there may be a workaround.
If there’s just one connection (or a set of connections) you would always like to be connected to when Studio 3T starts, you could enable Session Restore, which would restore all previously connected-to connections on startup.
Alternatively there are also our Quick Connect shortcuts: In the Connect dialog, right click on a connection (or a set of connections) and then assign one of the nine Quick Connect shortcuts. You can then hit Alt + 1-9 to quickly connect to your chosen connections from anywhere within the application.