Yes, if the food is not dangerously contaminated at the time of refreezing and is handled properly afterward. The only detrimental effect will be the one normally associated with freezing, a loss in texture and flavor - and it may be amplified.
The "do not refreeze" warning gained its prominence when Clarence Birdseye, the father of the frozen-vegetable industry, included the phrase on his company's packages. Business logic stood behind his decision. Birdseye did not want to be held responsible for any mishandling once the product reached the consumer's hands. If the customer repeatedly removed a package from the freezer, only to return it there after deciding it wasn't needed, the resulting textural damage would certainly discourage future sales. The frozen-food company also wanted to prevent customers from encouraging bacterial growth by subjecting the product to room temperatures for extended periods of time.
Some food writers interpreted the "do not refreeze" recommendation as a not-to-be-questioned health precaution, and the misapprehension quickly spread. However, it does not mean to suggest that foods should be randomly thawed and refrozen. Caution should always be exercised, especially since the injuries a food suffers during freezing and thawing make it more vulnerable to deterioration. Generally, you can safely refreeze a food that still has ice crystals, or that has been no warmer than 40oF and has been out of the freezer for no more than 24-48 hours. Shellfish and slices containing cream are among the foods that are particularly susceptible to bacterial growth. In most cases, they should not be refrozen once they have thoroughly thawed.
** Asian Recipes **