Well, I have never tried it, but I suspect you could not know if you got out all of the poison ivy roots. I think the only way to know if all the roots are out is if you manually pull them out by gloved hands. But using a mini tiller would probably be better than mowing them down, hitting them with the weed whacker, or pouring boiling water on the leaves. I don't think any of those other methods attack the roots, so the poison ivy would just regrow.
Again, I'm just talking aloud because I have no experience in removing poison ivy. I have been watching YouTube videos on removing poison ivy, and it appears to me that the "best" method is pulling out the plants by their roots.