And if it does does it proc for each tick of damage or on each reset? Does anybody know? I can’t find this info anywhere.
General rule of thumb.
Procs can’t proc procs.
In the case is BotS, it gives you one stack with each attack you make. Not sure how it’s applied with an AoE attack, but I do know only one mob will have the Stricken stack applied… As to which mob? 
So the answer to your question, is no.