Other Bob,

No, the O'Hare and similar sight micrometers will not work with the M1902 sight.  The M1902 is a tangent sight, similar to what is on most Mausers.  The M1901 sight is a ladder sight, very similar to the rear sight of the M1903 rifle: hence the O'Hare and similar adjusters will work.   

With the M1902 sight, you have only discreet, not continuous, elevation adjustments.  The size of the adjustments depends on the size of the serations on the sight.

To give you some idea of the scale of "coarse" vs fine adjustments,  here is a close-up pic of the side of a M1902 leaf with "coarse" serations:

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And here is a closeup of a M1902 leaf with "fine" serations:

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With coarse serations, you can make adjustments of 25 yards.  The value of that "25 yard" adjustment will vary with where you are on the sight.  Here is a table from an old source that gives some indication of what moving the elevation slide "25 yards" will do to your POA:

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You can get 1/2 of 25 yards, or 12-1/2 yards with the fine serations.  You'll have to do some interpolation as the Table only addresses 25 yard incremements.

In my one and only match shooting a M1898 infantry rifle at 600 yards (1977 or 78 ... will have to find the book), I used a M1902 rear sight with fine serations.  Other than one massive brain fart of moving the windage in the wrong direction, I did "OK"  ... 180 with a small X count.

Resp'y,
Bob S.