No.
Zero reading must be indicated only when the current through the coil is zero.
Equilibrium doesn't mean the net current is zero.
Equilibrium means the net torque is zero.
The deflecting torque which moves the pointer increases with current.
At the same time, the spring or phosphor-bronze fibre is twisted more and more and hence the restoring torque also increases.
When these opposing torques become equal, the pointer comes to a standstill, and we can easily take the reading.
Otherwise, the pointer would be fluctuating every now and then, and we wouldn't be able to record an exact reading.
When no current passes through the coil, no deflecting torque is produced, no rotation of coil, no tension in spring, no restoring torque, no movement in pointer.
Hope you're clear.