I wouldn't think so unless someone files a QA action against them with the other agency. Getting expelled from PADI is mostly about failure to follow PADI standards, and being unrepentant when caught at it. For instance, bad-mouthing PADI is against standards, and you may be counselled for doing it. If you then bad-mouth them again, you will be counselled in stronger terms. If you persist in bad-mouthing PADI, you will be expelled as a member. If you represent yourself as something you aren't (a DM parading as an instructor, for instance), you will be expelled.
None of those things are necessarily against the standards of other organizations. If you are looking for "unsafe" instructors to be expelled, well, that's almost as hard as firing a federal employee. The documentation of an instructor being unsafe would be onerous and isn't really what PADI is looking to fix, after all, if the instructor is following standards, by definition, they can't be "unsafe". So, for a person to be expelled from SDI or NAUI they would have to be teaching a SDI or NAUI class, violate standards, and refuse to be upgraded or re-taught. That doesn't happen for violating PADI standards.