This is WAY outside anything I really understand, but unfortunately I would guess not. There's an epithelial layer (the dental lamina) over the bone that generates teeth. I would guess that the peg is bonded to the bone itself (via hydroxyapatite) instead of any dental layers. Unless that layer can be regrown somehow, I don't think this would grow back your teeth.

I don't have any implants, but I do have several missing teeth. I had something like 14 teeth extracted, including all of my canines twice- I grew a third set. I think that probably wasn't as bad as getting implants, although I can still remember the feeling in my stomach every time they told me I needed more pulled. My mouth is just too small to fit more teeth so I don't think I'll ever have a full set either ¯\_(ツ)_/¯

What's probably more interesting is having the option of regrowing a tooth instead of, say, a root canal. Or just to replace teeth as they're worn down naturally.