As Mike and Marcia alluded to, in cases like this, the appraiser has two separate responsibilities: 1) form a reasonable opinion of value and 2) report pertinent information to the lender.
First, whether the loan is for a purchase or to refinance, the appraiser's job is to decide how much a typical buyer would be willing to pay for your property (usually by showing how much buyers did actually pay for similar properties) and to document the process and data that was used to form that opinion.
An appraiser would love to show prices paid for homes exactly like yours, in exactly the same condition and with exactly the same unfinished work. But, when there are no recent sales of exactly similar homes, the appraiser will analyze comparable sales and estimate the typical buyer's reaction to the physical differences between your house and those that sold recently.
Different markets will have different circumstances, so there is no consistent formula for determining the impact of unfinished projects. It's relatively easy to figure the cost to complete the work, but the appraiser must also estimate the additional discount expected for a less-than-perfect house. Sort of like a brand new car with a door ding - most buyers would demand a huge discount if the car is anything but pristine. And, just like car buyers would want more than just repair costs, the hypothetical buyer of your house is going to want more than just the cost of new carpet and tile. They'll expect a discount for their time and trouble and will approach the rest of the house with a more suspicious eye.
Second, in addition to the opinion of value, lenders require additional information that will be used in deciding whether the property is eligible for a specific loan program. The second factor involves the lender's policy regarding repairs, condition, etc. The appraiser must accurately report any observed (or known) problems with the property, whether they have an impact on value or not. If the appraiser suspects additional problems, they may even require that other professionals to inspect the property. Most lenders won't loan on properties that have existing health/safety problems or building code violations, but policies vary between lenders and it is often luck of the draw whether an underwriter gets picky or not.
As you can see, it depends on the specifics of your deal as well as a roll of the dice. You can significantly better your odds by spending some time finding an experienced loan agent who is intimately familiar with your local market and your situation. Every loan agent will say that they're the best, but many will waste your time and money preparing packages for lenders that won't even consider lending to you. A good one will quickly recognize the important factors and know which lender will be best for your situation.
