user4418: Article 8.1a states that:

In the course of play each player is required to record his own moves
  and those of his opponent in the correct manner, move after move, as
  clearly and legibly as possible, in the algebraic notation (Appendix
  C), on the ‘scoresheet’ prescribed for the competition.

Appendices C2 and C3 state:

C.2  Each piece is indicated by an abbreviation. In the English
  language it is the first letter, a capital letter, of its name.
  Example: K=king, Q=queen, R=rook, B=bishop, N=knight. (N is used for a
  knight, in order to avoid ambiguity.)
  C.3 For the abbreviation of
  the name of the pieces, each player is free to use the name which is
  commonly used in his country. Examples: F = fou (French for bishop), L
  = loper (Dutch for bishop). In printed periodicals, the use of figurines recommended.

Hence foreign languages and, indeed, foreign alphabets are allowed in the part of the notation denoting the piece moved. I believe I've seen Greek letters for pieces in a top level scoresheet.
However, C5 states:

The eight files (from left to right for White and from right to left
  for Black) are indicated by the small letters, a, b, c, d, e, f, g and
  h, respectively.

C7 goes on to state:

As a consequence of the previous rules, each of the sixty-four squares
  is invariably indicated by a unique combination of a letter and a
  number.

and then goes on to give a picture of a chessboard with the squares annotated with a1 through h8.
No allowance is made here for use of foreign alphabets and indeed in the aforementioned scoresheet that I saw the letters a through h were used for the files.
Am I correct in believing that the effect of these rules is that while native Russian, Greek, Arabic, Hebrew, Thai, Hindi, etc. speakers may use the standard abbreviations for the pieces in their own alphabets they must use the Latin letters a through h for the files rather than, for instance, alpha, beta, gamma, delta etc. for a Greek person?

user8860: Russian algebraic notation uses Roman letters a-h.  Hebrew does use א (Aleph) through ח (Ḥet, the 8th letter).  It would be awkward to mix Hebrew letters, normally read right-to-left, with Roman, read left-to-right (as is Cyrillic).  Yes, the Aleph column is still on the left, even though this makes columns a-to-h appear as א-to-ח in most diagrams, reversing the usual reading order.  (In actual play White sees the columns in reverse order, but Black sees them in natural order -- so on average it's a wash.)

user4418: There was an International Arbiter at our club annual rapid championship last night and when I asked him this question he was rather dismissive, I'm afraid. The rule is not intended to discriminate against speakers of languages with non-Latin alphabets and of course they may also use their alphabet for the files.

user3774: As a native Russian player I may assure you that we always used the suggested notation, e.g. Фd4 or Лd1 (Ф - ферзь - for Queen, Л - ладья - for Rook, etc); even the 6 years old beginners did so. Nobody ever was insane enough to suggest Russian alphabet for encoding files.

4418: <p>Article 8.1a states that:</p>

<blockquote>
  <p>In the course of play each player is required to record his own moves
  and those of his opponent in the correct manner, move after move, as
  clearly and legibly as possible, in the algebraic notation (Appendix
  C), on the ‘scoresheet’ prescribed for the competition.</p>
</blockquote>

<p>Appendices C2 and C3 state:</p>

<blockquote>
  <p>C.2  Each piece is indicated by an abbreviation. In the English
  language it is the first letter, a capital letter, of its name.
  Example: K=king, Q=queen, R=rook, B=bishop, N=knight. (N is used for a
  knight, in order to avoid ambiguity.)<br>
  C.3 For the abbreviation of
  the name of the pieces, each player is free to use the name which is
  commonly used in his country. Examples: F = fou (French for bishop), L
  = loper (Dutch for bishop). In printed periodicals, the use of figurines recommended.</p>
</blockquote>

<p>Hence foreign languages and, indeed, foreign alphabets are allowed in the part of the notation denoting the piece moved. I believe I've seen Greek letters for pieces in a top level scoresheet.</p>

<p>However, C5 states:</p>

<blockquote>
  <p>The eight files (from left to right for White and from right to left
  for Black) are indicated by the small letters, a, b, c, d, e, f, g and
  h, respectively.</p>
</blockquote>

<p>C7 goes on to state:</p>

<blockquote>
  <p>As a consequence of the previous rules, each of the sixty-four squares
  is invariably indicated by a unique combination of a letter and a
  number.</p>
</blockquote>

<p>and then goes on to give a picture of a chessboard with the squares annotated with a1 through h8.</p>

<p>No allowance is made here for use of foreign alphabets and indeed in the aforementioned scoresheet that I saw the letters a through h were used for the files.</p>

<p>Am I correct in believing that the effect of these rules is that while native Russian, Greek, Arabic, Hebrew, Thai, Hindi, etc. speakers may use the standard abbreviations for the pieces in their own alphabets they must use the Latin letters a through h for the files rather than, for instance, alpha, beta, gamma, delta etc. for a Greek person?</p>
 8860: <p>Russian algebraic notation uses Roman letters a-h.  Hebrew does use א (Aleph) through ח (Ḥet, the 8th letter).  It would be awkward to mix Hebrew letters, normally read right-to-left, with Roman, read left-to-right (as is Cyrillic).  Yes, the Aleph column is still on the left, even though this makes columns a-to-h appear as א-to-ח in most diagrams, reversing the usual reading order.  (In actual play White sees the columns in reverse order, but Black sees them in natural order -- so on average it's a wash.)</p>
 4418: <p>There was an International Arbiter at our club annual rapid championship last night and when I asked him this question he was rather dismissive, I'm afraid. The rule is not intended to discriminate against speakers of languages with non-Latin alphabets and of course they may also use their alphabet for the files.</p>
 3774: <p>As a native Russian player I may assure you that we always used the suggested notation, e.g. Фd4 or Лd1 (Ф - ферзь - for Queen, Л - ладья - for Rook, etc); even the 6 years old beginners did so. Nobody ever was insane enough to suggest Russian alphabet for encoding files.</p>
