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Something like this ?

tell application "OmniOutliner Professional"
	set intChars to 0
	tell front document
		repeat with oRow in rows
			repeat with oCell in cells of oRow
				if type of column of oCell is rich text then
					repeat with oText in text of oCell
						set intChars to intChars + (count of characters of oText)
					end repeat
				end if
			end repeat
		end repeat
	end tell
	display dialog (intChars as string) & " characters"
end tell