It should work fine if all parts are within specifications on any Picatinny front/bottom rail. Here's another photo from Wilson Combat which shows the metal piece screwed in, tightening the fore-grip to the rail.
I'm a bit confused by your question, however. Isn't the Tapco T6 a collapsible buttstock? A vertical fore-grip isn't made to attach to a buttstock nor does that buttstock have a Picatinny rail.
