I'm not an immunologist, but I'm pretty sure that's not how RNAi would work. RNAi is mediated by RISC, which requires certain features of small RNA and certain mediator proteins to target and silence complementary mRNAs. RNAi isn't just the hybridization of two mRNAs to form a double-stranded molecule (which would be degraded by ribonucleases anyway).
The Pfizer and Moderna mRNA vaccines are specifically designed to look like cellular mRNA, with optimized UTRs, ribosome binding sites, and minimized secondary structures. Some of the bases (e.g. uridine to pseudouridine, etc) have been modified to mimic cellular RNAs as well in order to minimize the cell's foreign nucleic acid responses. If anything, the real risk is that the mRNA will be "caught" by the cell and immune system and subsequently degraded. People could worry more about allergic reactions to the lipids encasing the mRNA or the carrier solvents of the actual vaccine (not that those are huge concerns anyway).
