From what I have heard this might make the Net Price Calculator less than fully reliable. Unfortunately financial aid can be more difficult to predict in these complicated situations (and it is beyond my ability to guess what the result might be).
If the NPC shows a net price of $45,000 per year, and it actually comes to full price at roughly $84,000 per year, this is a valid reason to break the ED agreement. However, you might want to be prepared in case this in fact happens. Of course you already need to be prepared in case you do not get into Dartmouth ED (or any other choice ED).
Also, I agree that you need to be fully prepared to fund a full 4 years at whatever university you attend before you decide to go there. It might be even better to be able to fund 5 years in case something goes wrong or changes (a dual major or late change in major for example might not count as “going wrong” but might nonetheless delay graduation).