Answer
No.
Work Step by Step
Linear momentum is a vector, pointing in the same direction as the velocity vector, $\vec{\mathrm{v}}$.
Kinetic energy has no direction. It is a nonnegative scalar.
We can have two nonzero vectors whose sum is zero.
For example, take two particles with the same mass moving in opposite directions with same speeds. These particles have equal magnitudes of momentum. Their momentum vectors add to 0.
The kinetic energy of each particle is positive, so the kinetic energy of the system is nonzero. The sum of the momenta is zero, but the sum of kinetic energies is not.
