Well this is embarassing. I've answered my own question. Yes the part is fully static and can tolerate the clock stopping between ending a command and reading the results. I had it in my head that there was a non-zero value in the status register at powerup. Wrong. I was indead reading the status register and it's value was zero. As soon as I wrote a WREN command (write enable) and read the status register I got back a value of two.
After that everything works fine. Thanks for the time and sorry about the noise.