Yes, of course the possibility is there, but it needs a huge leap of the imagination to even hypothesise what that short or long term adverse effect from mRNA vaccinations could be. Don't forget that coronaviruses are themselves "mRNA vaccines", with the significant difference that they actually reproduce, are contagious, and cause disease.

One could also argue that there's the possibility that SARS-CoV-2 will trigger an epidemic of extreme early-onset Alzheimer's in people who are currently suffering from long COVID. I don't think this is likely either, but I would argue it's significantly more so than an abstract unknown unknown about mRNA vaccine side effects surfacing in the future.