There is a difference between "can" and "should". The missing permit should not prohibit you from purchasing the home unless the lender cannot value the home at the agreed to purchase price due to the variance in square footage or integrity of the property.
As long as you are aware of this permit issue, the burden falls on you as to whether you are willing to take on any risk involved if the city or county were to require you to obtain the necessary permits by the use of a licensed building contractor.
Caveat emptor is latin for "Buyer Beware" and certainly comes into play for you on this one. Best of luck to you!
Diane Wheatley, Broker
Jack Gillis, M.B.A., J.D.
Jack Gillis Realty Advisors
Nathan Grace Real Estate, Broker
5619 Dyer Street | Suite 100
Dallas, TX 75206