I just discovered one of my CD players is able to do it. I have checked have only checked Demolicious so far, which had no pregap songs on it. I will check the others on either tomorrow or on Friday.
Tonight Alive's What Are You So Scared of which was released in 2011 has 10 pregap acoustic versions of songs on the main part of the album.
I ended up buy the Dos vinyl today. It only arrived at the record store on Friday, but I have no idea when it was pressed, but it still has Drama Queen on it. Only information about pressing details is that it was made in the US and that it was Reprise not Adeline that pressed it. I am pretty new to vinyl so I might be missing something that indicates a pressing date.