Alpha-gal is a sugar, so this wouldn’t work directly. Also, the syndrome seems to be IgE-mediated, and the mRNA vaccines are intended to induce IgG and perhaps IgA production. So this might not work.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6554561/
Alpha-Gal syndrome is characterized by IgE (allergic) antibodies, and the mechanism that induces them is complicated. Merely putting an antigen into your body doesn’t do it.