this is hard to say yes, but i can tell you that the live virus will replicate in the cell and increase copy number of its RNA until the cell dies. the vaccine mRNA will remain until degraded and stop producing valid copies.
the vaccine is not the whole mRNA, its only the part that codes for immunogenic protien [SARS-2 S] that is exported to the cell membrane
I'm no expert either, but I don't see a difference here between virus infected cells and mRNA "infected" cells. So cells primed with mRNA simply produce less virus parts than those with the real virus?