can global index be alter to invisible?

RDBMS 11.2.0.4, need to evaluate if a local index will bring better performance than the current global index, we plan to alter the global index to invisible, and then create a new local index with additional column, if the local index does not bring better performance, we will simply drop the local index and alter the original global index to visible. I was told that global index cannot be alter to invisible, but was not find any doc to confirm this.  The following test case shows it is feasible though

create table test (id number, col1 varchar2(10))

tablespace users

partition by range (id)