Will dishonesty show in writing?

Oooh yes, but unless the graphologist works with law enforcement in some way they generally don't see the really glaring stuff. But, we see the signs that show you deceive yourself and do not want to face things you find unpleasant. Or the person who talks around their issues. They drop hints that may be so broad you miss them and then get angry because you missed a birthday or occassion they felt was special. When I do a quickie and find this I tell the writer "You can't assume the people around you always know what you are upset about. They can't read your mind so you must learn to be more direct and talk to them. You can't tell your friends, family, neighbor, kids, you'd like to attend a concert, go to the movies, its your birthday and expect them to tell your spouse. You must do it and don't just leave notes or drop hints. Tell them and make plans together."
Then too we see the person who will lie by omission or never answer a question if they can help it. Their usual response is to answer with another question. "Why would you ask that?" " Do you need it now?" " What keys?" or just "Why?" You know those people I am sure. I always told my teacher he should have been a psychiatrist because he always asked "What do you think?" or "How do you feel about that?" It drove me crazy because I wouldn't ask if I didn't need an answer or at least a hint of where to look for an answer.
There are also the little white lies we have to tell on a job. "The boss isn't in just now." "Mr. xxx is in a meeting can he call you back?" "Oh, sorry I have an appointment on that day." We all do it at times so it will show up in the writing. Remember the secretary I mentioned. She said looking through her book she could see the times she had to give an evasive answer to a caller.