Yes, it's a perfectly probable consequence of a host of physiological & psychological factors, namely, my bum is being whacked, I am forced to adopt a revealing posture, the cane (or whatever implement) is hitting close to my genitals & I have not peed [or allowed to pee] before my punishment & I am scared as hell.
What else can happen except a little stream?
Grin & bear it, you naughty little girl!
