it process >> like the shell without invoking the shell

No.

$ dir foo
ls: foo: No such file or directory

$ perl -MIPC::System::Simple=systemx -e'systemx "ls", ">>", "foo"'
ls: >>: No such file or directory
ls: foo: No such file or directory
"ls" unexpectedly returned exit value 2 at -e line 1

$ perl -MIPC::System::Simple=systemx -e'systemx "ls >> foo"'
"ls >> foo" failed to start: "No such file or directory" at -e line 1

$ dir foo
ls: foo: No such file or directory
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Same goes for 2>&1

$ perl -MIPC::System::Simple=systemx -e'systemx "ls 2>&1"'
"ls 2>&1" failed to start: "No such file or directory" at -e line 1

$ perl -MIPC::System::Simple=systemx -e'systemx "ls", "2>&1"'
ls: 2>&1: No such file or directory
"ls" unexpectedly returned exit value 2 at -e line 1
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It would defy the entire point of systemx if any argument was treated specially.