It seems to have nothing to do with long paths or non-latin characters:

use strict;
use warnings;
use feature 'say';
use Spreadsheet::Read;
use Spreadsheet::ParseExcel;

open my $h, '<', '1.ods';                       # this file exists

Spreadsheet::ParseExcel-> new-> parse( $h );    ####
say 'eof' if eof $h;
say 'ok'  if defined ReadData( $h );
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says 'eof'. But if line marked with '###' is commented out, the output is

Sorry, references as input are not (yet) supported by Spreadsheet::Rea
+dSXC at xl.pl line 11.
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So, the reason that you can't supply filehandles to Spreadsheet::ReadSXC is because it doesn't support them. And there was no proper error reported for your example, because of this line -- and that line wasn't reached.

Copying to a temporary safely named file can solve it:

use strict;
use warnings;
use feature 'say';
use utf8;
use Spreadsheet::Read;
use File::Temp;
use Win32::LongPath;

my $tmp = File::Temp-> new( SUFFIX => '.ods' )-> filename;

copyL 'проверка.ods', $tmp;                 # this file exists

say 'ok' if defined ReadData( $tmp );