I did my entire installation with no tape or glue. I have never had any trouble with it blowing up or moving, unless I pull it up.
But, to answer your question, there is no reason the double-stick would not work. The only areas that it would be needed are the very front, center carpet above the tunnel and against the firewall, and then the forward, top kick panels on each side. I was able to wedge mine in in those area, and they stay put without any stick-um. Other areas that could cause problems use snaps to hold it, like the tunnel and floors.