One of the idea with “has the space around it cleared” is that the body has the right size and gravitational pull. The theoretical object in the Oort Cloud would relative fast clear the space around himself if it had the size to have a stable and long living internal heat source (that would either need lots of decaying nuclear material or would need to be at least about earth size to have enough stored energy to have a molten core).

So if you put earth into the Oort Cloud it would still be a planet, because we know that earth has the potential to clean it’s neighborhood. Not that our definition would be relevant, because Earth in the Oort Cloud would be a lifeless rock very fast, with nobody left to care about definitions.