The vorlauf will help you eliminate chunks of grain & husk that could otherwise add tannins, get scorched, or promote additional matter that you don't want/need.
I use a 10-gallon Rubbermaid cooler with stainless braid.
I typically run 2 to 3 quarts, because I run into a gallon pitcher & there's room to do so.
I place a receiving kettle under the tun, place my gallon pitcher into the kettle & put the hose into the pitcher.
When the runnings look quite clear, I drop the hose into the kettle & very slowly pour the initial runnings into the rear of the tun.
HSA isn't going to occur from the mild treatment involved in most vorlaufing.
But, you could possibly be pushing your luck with that straining method.
That said...I believe HSA exists, but have never noticed it in my brews, or anyone else's.
...Kinda like the way I believe in sasquatch.