My understanding is that this is indeed what happened. I believe it was in the "A Time To..." series that establishes that Min Zife was forced to resign (read: assassinated) over the Tezwa affair, and Bacco won the special election to replace him. This all took place just days before Shinzon and Tal'Aura wiped out the Romulan Senate. I am also of the understanding that the Federation presidency has no term limits, given that the STO timeline establishes Bacco serving until 2392, which would imply at least three full terms.