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There are two answers to your question, and they depend on whether we're talking about electrostatics or electrodynamics.

Electrostatics:No. In the absence of a varying magnetic field, the electric field intensity is equal to just the negative gradient of the electric potential; E = -∇Φ. So, if Φ is 0, its gradient, which is just the vector field made from the partial derivatives of Φ, has to be 0. The reverse, however, can happen. E can be 0, but Φ doesn't have to be; it can also be a non-zero constant. Electrodynamics:Yes. In the presence of a varying magnetic field, E = -∇Φ - ∂A/∂t, where A is the magnetic vector potential, and t is time. So, if Φ is 0 this time, E can still be equal to the possible non-zero term, -∂A/∂t.
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