“Absolutely” it is possible — if the Chrome developers would do something so utterly foolish as to spend hundreds of hours writing an API emulation layer for Chrome, add tons of hooks into the base browser code to support the emulation layer, add massive code bloat, slow the browser, find some way to make this jive with their multiple-process execution model, probably only work with a limited number of extensions, and saddle everything they do to the design decisions that Mozilla may make in the future. In short, yeah, if they re-write Chrome to be no different than Firefox, and thus erase it's entire reason for existing, it would work.
How in blazes are “installed by the end user” and “deeply tied to Mozilla's internal API” contradictory? Do you even know what an XPI is? Evidently not. Go Google it and stop making such a fool out of yourself.