No. You can use SQL Server Management Studio on Windows to manage SQL Server on Linux but the software itself needs Windows. The link from Microsoft does have a tip about a new tool that can:
Tip
If you do not have a Windows machine to run SSMS on, consider the new SQL Server Operations Studio. It provides a graphical tool for managing SQL Server and runs on both Linux and Windows.
SQL Server Operations Studio is currently only available as a preview but does have a download to a DEB installer.
Installation after downloading the deb:
cd ~
sudo dpkg -i ./Downloads/sqlops-linux-<version string>.deb
sqlops