No. A piezoelectric single crystal need not be ferroelectric. A noncentrosymmetric crystal can couple strain to polarization without having a spontaneous polarization that an electric field can switch. Quartz is a standard example.
A single crystal already has an oriented crystallographic tensor, so the random-grain cancellation issue does not arise. The relevant tests are crystal symmetry and the nonzero piezoelectric coefficients; ferroelectric switching is a separate property.

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