Spontaneously, yes - fairly amazing. But what if the person treated with the mRNA vaccine happens to be infected with another RNA virus that is producing reverse transcriptase enzymes to convert its own RNA into DNA?
To prevent an immune response and degradation, the mRNA vaccine nucleosides are modified from normal human mRNA. It's possible that RNA virus reverse transcriptase may not be able to work on these modified nucleosides.
https://www.nature.com/articles/nrd.2017.243