MS SQL running out of Disk Space - can FileGroups be used to free up some space?
While it will work, it's not necessary to move tables to a new filegroup.  

If you simply add a file to the database's existing filegroup(s) SQL Server will start using the new file(s).

SQL Server uses a "proportional fill algorithm" when a filegroup has multiple files.  So if you add a new file (perhaps on a different volume) to a filegroup, SQL Server will write new data to that filegroup until it's the same percentage full as the current file.