Backing up Oracle home directory while instances are running
Yes you can do that. There's nothing dynamically changeable here in normal circumstances. All the files here are not touched except in case you apply some patch.

Files specific to the particular database resides in:

$ORACLE_HOME/dbs
$ORACLE_HOME/network/admin


I do that now and then to create test environment. Just for such more complex directory structure I prefer rsync. With it you can resume copying if you run into some disk space or network issues.