Yes and no.

Yes because we can calculate it easily if we pretend the nucleus is classical, not a quantum object. This should be a good approximation. But I'm not sure there's any measurable consequence of this tiny force which will be dwarfed by electromagnetism at that distance.

No because no one knows how to get gravity to work on a quantum scale, so good luck computing gravitational effects due to quantum objects. We also can't measure it to check, since it's so tiny compared to other effects.