Yes, If you choose to re-apply even include a semi-detailed budget and day-to-day itinerary. To strengthen your profile. Put more information in regards to you having to go back to school...If that's the case. If you pay rent, and in a lease, add that. Think outside of the box with reason of course. But just prove you are a genuine visitor, AND you have all reason to return home.
I'm afraid that if you re-apply with the letter it may come of as deception. So unless you have a good explanation then don't add it.
I applied for my boyfriend. He was refused but I managed not to get the refusal for Home ties. He has a daughter and mother he'd be leaving home. So that did not affect us. Just financial,purpose, and travel history.
I have re-applied and I am waiting to see what happens.