No. Illegal procedure, illegal motion or an illegal formation does not blow the play dead - only a false start or delay of game against the offense will do that. (Or, encroachment against the defense or offsides unabated to the QB. Also, a neutral zone infraction will blow the play dead).
On the fake FG it wasn't a false start, it was officially called illegal motion (even though just about everything was messed up), so the play continues as normal then the defense can choose to accept or decline it. Since the Patriots got the first down (after the review), the obvious decision is to take the penalty.