No, according to Barry Eichengreen, Cevat Giray Aksoy, and Orkun Saka:
It is sometimes said that an effect of the COVID-19 pandemic will be heightened appreciation of the importance of scientific research and expertise. We test this hypothesis by examining how exposure to previous epidemics affected trust in science and scientists. Building on the “impressionable years hypothesis” that attitudes are durably formed during the ages 18 to 25, we focus on individuals exposed to epidemics in their country of residence at this particular stage of the life course. Combining data from a 2018 Wellcome Trust survey of more than 75,000 individuals in 138 countries with data on global epidemics since 1970, we show that such exposure has no impact on views of science as an endeavor but that it significantly reduces trust in scientists and in the benefits of their work. We also illustrate that the decline in trust is driven by the individuals with little previous training in science subjects. Finally, our evidence suggests that epidemic-induced distrust translates into lower compliance with health-related policies in the form of negative views towards vaccines and lower rates of child vaccination.
Here is the link to the NBER working paper.