Something like this ?
Code:
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