Did the SPCA ever go looking for this Shrodinger cat?

Yes, the Serious Physicists' Curiosity Association looks for Schrodinger's Cat all the time, and they often find that the cat is in two different places.

They have been unable to determine if the cat is actually alive or dead.  Every time they open the box they get a different result.

What most people don't realize is there are 6 possibilities, not 2.
Live/dead In, Live/dead out the box, Live/dead partially out of the box.
IF you specify there is a cat in the box, that limits you to two possibilities.
My cat named Shrodinger is alive and well, neutered and fully vaccinated!

Sure, Society for the Prevention of Cruelty to Animals is still looking for that poor pet 

Schroeder's Cat.  Stupid.

Idiot troll .....

troll, go away      

Yes, I think they found he was still in the box with the probability still t0 be determined about whether he was dead or alive.

No, the SPCA does not respond to dead/live cats.