My understanding's that fever's an immune system response to pathogens. Would suppression of this response delay time to recovery?
There are studies that state reducing a fever may prolong illness. Fever can increase T-cell proliferation and cytotoxic activity. A study in 1990 showed that acetaminophen and aspirin increased symptoms and made viral shedding last longer. While that doesn't exactly address the role of NSAIDS I would think it would be the same as aspirin and acetaminophen. Source: Is Breaking the Fever Bad? Fever Suppression May Be Detrimental by Catherine Moss