Do you have to read the notation differently?
Obviously the notation says what notes are to be played. That's what you play. On any guitar tuned any way. What can't happen is that you assume the guitar is in standard tuning, and play where the notes would have been found. Because they won't be there!
For example, if the guitar is tuned down by a tone for each string, then all the written notes would have to be fretted two frets higher than normal. If it's completely different, each note will be found on a different fret/string compared to standard tuning.
It certainly wouldn't be read differently - the notes won't alter, but it'll be fingered differently.