I would question scheduling and attendance in a shared arena. Oh, sure, the hype of a new place would initially spike the numbers a little bit, but after a while, getting students off campus to a game would begin to wear. We saw that when the Hornets played at the Auditorium. TV might not want to show a game where fans are disguised as empty seats.
The scheduling, however, may be the bigger issue. The Kings, clearly, would have priority, and conflicts may arise, particularly given that Sac has TWO hoops teams. (It wouldn't be very fair to leave the girls in that jr high POS we have now if the guys get to move. Gymnastics would also be an issue (a minor one, I grant you). VB probably wouldn't be a big deal given that the vast majority of their season (and perhaps all of it) would take place before the Kings take the court. In fact, starting a pre-season VB tournament could draw in badly needed funds.
Another factor is off-season event scheduling, particularly concerts. This is another reason why an on-campus arena is so vital. If we have our own arena, we control the revenue. If we share it with the Kings, does anyone really expect the Maloofs to let us share those revenues? I think not.
So, if the two sides can work out an adequte scheduling arrangement (both the NBA and the Sky would have to be involved), it MIGHT work, IF we can get fans there. A free shuttle from the dorms could be the answer. An interesting idea, to be sure.