There is a chance the lender will not lend you the necessary money to purchase in that situation. Many real estate agents in the state use standard purchase and sale agreement forms published by the Northwest Multiple Listing Service (NWMLS). One of those forms is something called a Financing Addendum that addresses this situation. That form—or some other Financing Addendum—should be used where you are depending on financing to purchase the home. The NWMLS addendum provides a process where if the appraisal comes back less than the purchase price, there may be an adjustment of the purchase price.
Secret transactions outside of the purchase and sale agreement are always a concern and something you really should stay away from.
Even if you are working with a real estate agent who is probably using the NWMLS forms, you really should spend a little bit of time talking with attorney about what the agreement sign before you sign anything. The attorney can explain to you the process provided in the form/addendum you are signing. If you are not working with an agent, you definitely should have an attorney prepare the agreement for you. The cost of doing so is often less than many people think, and it is worth the cost for such a large purchase.