No. But you can add their locations to the app by tapping your station name at the top and then tapping the + in the top right corner to add a location.
If you want to see all the detail from other stations just use the link to the stations like you would any other station. You can share a station link by using the share icon at the bottom of the screen in the Tempest app.
Note that the station needs to be marked publicly accessible to be viewed by others. This is the default.