No, at least not as desired.

• There are two elements in each record, 0 and 1, yet you address 1 and 2.

• One of the two elements is a string, yet you use the numerical compare (<=>) operator. Use the string one instead (cmp).

• [stat]->[9] is needlessly slow. Use (stat)[9] instead.

• You didn't specify how the string should be sorted, but I'm guessing you want to sort by mtime first, and by name last.

If my guess is correct, you get:

my @sorted_files_Test_flat_file_write_over_name_only =
   map  { $_->[0] }
   sort { $a->[1] <=> $b->[1] or $a->[0] cmp $b->[0] }
   map  { [ $_,  (stat)[9] ] }  
   @files_Test_flat_file_write_over_name_only;
[download]

or the faster

my @sorted_files_Test_flat_file_write_over_name_only =
   map  { substr($_, 11) }
   sort
   map  { sprintf('%011d%s', (stat)[9], $_) }  
   @files_Test_flat_file_write_over_name_only;
[download]

Update: Formatting changes. Added code.

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