A conventional pea whistle is, acoustically speaking, a vessel flute. The same as an ocarina, and obeys the same equations as an vessel flute. Even with the pea jammed in place, or removed altogether, it will generate a steady tone. I had a couple of de-pea'd (neutered?)whistles, and aside from having a lowered pitch, work as well as the unaltered models.
That's good info, thanks.