You're talking about giving no notice, and actually working for a second carrier while you're drawing wage or benefits from the first?
You're concerned about the legal or the ethical incorrectness of this act?
It's rhetorical. That you're considering it makes clear that you're not concerned that that this is unethical, and if you don't see why, there's little sense attempting to explain it to you. That you're asking in a legal forum makes clear that you are concerned whether the matter is legal, which begs the question how you could ask if something's legal yet have no ethical concern.
What regulation do you think might be violated by working under more than one certificate holder?
There is no legal violation directly, as a number of alirlines employ contractors or direct instructors/check airmen on a part time basis or full time, but who moonlight doing work for other operators. I recently trained with one who works for two different airlines. He does so with full knowledge of both, however, and is authorized by both operators to provide those services.
There are companies which have requirements as policy that you work for no other operator while working for them; outside flying employment is prohibited by company policy, rather than by FAA regulation. When you violate that policy, you're subjecting yourself to actions outside administrative law (FAA); you're potentially treading on a civil matter, and could get yourself fired by the first airline (or the second) if found to be violating policy.
Why might the company(ies) fire you? See the ethical question implied at the outset. Again, would you really be asking if it's wrong on any level if you didn't believe so? That should tell you something.
Consider the implications of a firing and the impact it might have, and weight that in your decision. It's evident you're thinking of taking that chance, making your call a calculated one, yet it bears mention anyway.
Having said this, my response above does not consider additional unmentioned factors, such as operating on saved sick leave or other time; if you're in a situation where your company could not use you because you're burning off two hundred days of unused sick time or vacation days, or something else of that nature, then you have never been in a position prior to your resignation in which you may have been called upon to work for your present airline. The ethics of no-notice resignation while working for another carrier is still questionable and still looks bad, but is explainable on some level. Again, calculated action on your part, perhaps, but be careful. While not necessarily legal jeopardy, and justifiable by circumstance to you personally, it may not be viewed that way by either employer. Your second employer may not care that you're still on the books for the former; some may, some may not. I suspect that your former employer, however, would not be nearly so apathetic.