Yes, you can!
I did a battle right now but forgot to upload replay, but I binded and then Snap Trapped and it worked. Snap Trap didn't fail, but it only shows a red "Bind" icon on the opposing Pokemon. They will stack and do more damage. Two binding moves, however, is not very viable. It will do more damage if you have it hold the Binding Band, though. You only need one binding move, you don't need two. It will stack and do more damage, though.
Hope I helped!