Possibly, but I wouldn't allow it.

While this may not be against the exact wording of the class ability, it is pretty clearly against the intent that your arcane armor is your one and only armor. As a DM, I wouldn't allow you to do this.

Possibly, but I wouldn't allow it.

As you said, Arcane Armor stops being arcane armor if you put on another suit of armor (or die).

Technically speaking, in the scenario you describe, you aren't donning any armor after the Arcane Armor, so you haven't run afoul of the exact wording of the class ability. However, I think this is pretty clearly against the intent that your arcane armor is your one and only armor. "The artificer bonds with this armor, becoming one with it...", and they included a specific rule that you can't even put on a different suit of armor without screwing up that bond.

The flavor and design of the class are that your Arcane Armor is special, so bypassing that by slipping around the exact language is just cheesy. As a DM, I wouldn't allow you to do this.