Capacitor Charge Sharing
No, not correct because the 1V precharge of C1 is able to overcome the 0.25V of the supply. Since C1 acts like a DC blocker, once C1 and C2 equalize in voltage it will just there. It's kind of a weird scenario and I'm having some trouble thinking about it.

But the end result should be as if C1 and C2 are connected in parallel with both bottom plates connected to GND. The top plates will both reach some voltage less than 1V due to the finite charge available from C2's precharge redistributing voltage. However, C1 will hold less charge than it would if its bottom plate were actually connected to GND since its negative terminal has been lifted above ground by 0.25V/0.35V. In effect, C1 would appear as a smaller capacitor whose bottom plate was connected to GND.