Yes you can use Online backups when TRACKMOD is on (LUW).
You did not mention the operating system, but for LUW the trackmod is a database level configuration parameter (i.e. is not tablespace specific).
Besides, why would you quote a Micro Focus page instead of an IBM page ?
A possible reason that Micro Focus includes that information is that Micro Focus sells solutions for COBOL that often involve offloading from mainframe COBOL - and on DB2 for Z/OS the TRACKMOD is a tablespace specific property.
However, on Windows, Linux, and Unix the TRACKMOD is at the database level as previously stated.