Let's say someone were holding an object (like a pencil) at a position away from the centre of mass, such that it would rotate from the gravitational torque if held still. Would there be a way to spin it (as in, about an external axis, while the line from the centre of mass to the pivot is in the same direction as the radius) such that the torque from the centripetal acceleration would just cancel out the gravitational torque?

yes, this is a common demonstration in angular momentum and couples. It is known as Induced rotation or precession.

torque from the centripetal acceleration

 

There can be no such thing. Centripetal acceleration is by definition radial, so r x F = 0. To exert a torque you need a non-radial force.