Float operations will probably NOT be identical on different CPU flavors. The reason is register size. Intel-derived processors (like AMD) use 80-bit registers for float arithmetic, and so operations that are optimized to be accumulated in registers before being written finally back to 32-bit storage (say) will maintain more accuracy than on a CPU with 64-bit registers (like SPARC).

Even on the same CPU, compiling the same code with different optimization levels or different compilers might lead to different register usage, and so different results.

Except in very unstable cases, the differences would be minor and shouldn't cause you to lose sleep. Instability might occur if, for example, there is a test like
  if( x < 4.0 ) x = 1.0 ;
so that for x=3.999999 the result is markedly different than if x=4.000001. 3dDespike shouldn't have such a sensitivity, though, since it doesn't crush spikes brutally as soon as they pass threshold, but pushes them down gently at first when just a little above threshold, and then more firmly when the spike is more above the threshold. In other words, 3dDespike's transformation of the data is supposed to be a continuous function -- if it were implemented in perfect arithmetic.