No the centre of mass would not accelerate,the object will rotate about the centre of mass.

Also see this : http://physics.stackexchange.com/questions/80544/why-dont-couple-forces-violate-newtons-first-law/80549#80549

Edit:If the object is on a table(or anywhere here on the earth) and if you apply the forces as shown in the fig it may not be rotated about the centre of mass because of the frictional forces acting on the object,but in space where there is no friction the object will rotate about the centre of mass.