I've heard of what you're describing being used for temp control, but not for limiting O2 penetration.
My understanding of the oxygen permeability of water based on the tables listed in this link
suggests to me that putting your fermentation bucket inside another plastic bin filled with water would be futile.
Creatures of the sea get plenty of oxygen from the water in which they swim, don't they?
Based on the table, completely saran wrapping (i.e., 'mummify") the plastic fermeter seems to be a better option if the goal is to limit O2 permeability.
Regardless, I've never heard of this being done. But it should be very easy to do. I'd appreciate it if others chimed in and gave their views.
It would actually serve both purposes - I've learned that in the summer my basement temp doesn't stay as consistent as in the winter.
The solubility of O2 in fresh water is around 9.1 mg/L (9.1 ppm) vs 21% (21,000,000 ppm) O2 conc. in air. That is, once water absorbs this much oxygen, excess oxygen in the air will not absorb into the water and "permeate" through to the bucket.
Submersing the bucket in water will limit O2 in the local environment almost completely. No oxygen outside the bucket = no oxygen inside the bucket (except for the lid, which will not be covered by water).