Yes, they can absolutely regrow after the leaves have been eaten, whether by critters or by you. If it is excessive, as in all the leaves or if it is repetitive the final yield will suffer of course.
I think their resilience in that regard is because sweet potatoes are actually storage roots. So long as they are well established they can rapidly recover from such damage as well as weather droughts and insects but each time they have to call on their stored water and nutrients it degrades the root. From my experience that degradation is in regard to size rather than quality.
Yeah, so, uh, I eat the leaves of my sweet potatoes all the time and they do just fine, so I think you're good!!
(I trellis mine specifically to eat the leaves. Every so often I harvest unintentional sweet potatoes, but we are after the leaves. Once they get going, it seems like sweet potatoes are pretty resilient.)
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