No, this has absolutely NOTHING to do with immobiliser. Bypass kit not required.
Although have just read your other thread..... rather than fit a bogus bypass thing just diagnose issue. Usually just a dead reader coil, or faulty chip.... if it's the latter just get a new transponder matched, anyone with VCDS or similar can do if you have the SKC.
Your problem with it staying is probably caused by a faulty ignition switch.... i.e. the electrical part of it (and usually only that in case you're thinking of getting the whole thing).
Replacement part is cheap but steering wheel needs to come off as well as bush behind it (puller required) so a bit of a fuff. Or other electrical fault or wrong connections made when transplanting engine.
