If the corp rezzed it on their turn, yes it stops the scoring off Sansan; councilman is not a paid ability, it’s a reaction ability so they can’t rez and score before you can use councilman. They can play around it by rezzing it at the end of your turn and re-rezzing again on their turn (provided you used councilman)
As with clot, if the agenda is ready to score (i.e, has all of it tokens), then the corp can score after the use CVS. If they don’t score in that paid abilities window (i.e., they cleared with CVS but did not score in that paid abilities window), then you have the opportunity to re-clot before they take their next click. That’s why you advance an agenda until you’re ready to score rather than trying to CVS early; you keep priority on paid abilities until you pass the window to the other player.
Side note: You can use sacrificial construct to prevent clot from being trashed (you trash sac con to prevent clot from being trashed by the purge), requiring 1 extra CVS per sac con.