Sure...if you use the adenavirus based vaccines like JJ. The pfizer and moderna don’t work like that.
@ mdmathis6
The article talks about both type of vaccines.
“SARS-CoV-2 RNA or segments of it, like the spike gene, can be reverse transcribed by LINE-1-encoded reverse transcriptases or other factors, and the thus synthesized DNA can become integrated at unknown frequencies and locations into the vaccinees’ genomes. Of course, the same is true for all SARS-CoV-2 infections. Hence, the risk of undesired integration events of SARS-CoV-2 RNA reverse transcripts upon SARS-CoV-2 infections appears similar to that upon vaccination with the mRNA-based Covid-19 vaccine.”