No, the expected amount of procs will be the same.
At no spool you should expect to see 4.4 * 310% = 13.64 procs. At full spool you should expect to see 12*4.4 * 310%/12 = 13.64 procs, since while your multishot increases by a factor of 12, your total status chance is divided by a factor of 12. 12/12 = 1
That's simply a side effect of Kohm's status chance being divided per pellet as it ramps up, even without modded MS you'd see the same effect.
You might be asking yourself what the benefit of fully spooling up is then...there isn't one as far as I can tell. The increased area is more than offset by the ammo cost, so in my opinion I don't think there is benefit at all. Idk though.