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No. In fact, the charge-charge interaction correction would vanish, as the charge density at the nucleus would equal zero if there is no overlap. Similarly, the current-current interaction correction would vanish, as there would be no Fermi contact contribution, since there cannot be any spin up-down imbalance at the nucleus, as there are no electrons in the nucleus.
The Bohr-Weisskopf effect would be observable also by comparing that nucleus with an isotopic form of the same nucleus.
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