While the answer to this question will depend on the probate laws of the state where the family is seeking to admit the copy of the will to probate, the general answer is yes, provided that very specific conditions are met. Why? Because it's assumed that if an original will can't be found, then the person who wrote it (called the "Testator") intended to destroy it.
Problems arise when the Testator's heirs at law or beneficiaries named in an older will are different from the beneficiaries named in the later will. If only a copy of the later will is located, then the beneficiaries of the older will can object to the probate of the later copy (particularly if they are able to find the original older will). But if all of the beneficiaries and heirs at law agree that the copy of the later will should be honored, then the probate attorney will be able to guide the beneficiaries through the steps necessary to get the copy admitted to probate.