Technically, it should be possible: Eliminate the family tree, eliminate the senate. But it's quite possible that the game automatically generates birth events as the fathers are slain, even if they're not married yet. Generating marriage events for 16 year olds and promoting the sons to age 16 just like that. Since there is no script or command to age a family member 16 years just like that, it must be concluded that SPQR uses "Man of the hour" events to trigger after their final member is assassinated.
Perhaps this is so the end-game is still preserved. Without a senate, there is no Outlawed! message. You can still declare war though on the other romans. But sooner or later you would need to conquer Rome. Ever tried making Rome rebel?
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