Fully submerged water bath for stove top baking?

Unlikely. Without even getting into the mechanics of how it would work, simple physics dictates that you can't get the temperature of this "immersion oven" above 100 degrees Celsius. Most cakes and breads are cooked at temperatures above 170 degrees Celsius. A second issue is that moisture can escape when baking in a normal oven. Your "immersion oven" would not allow steam to escape whatever you're cooking, which would lead to the contents being a bit steamed as well as baked. Sometimes this is desirable (see eg making bread in dutch ovens), but not for the majority of breads and cakes.

So normally, stove top cooking never results in all around heat like in an oven but what if you were to submerge (underwater bath instead of just around the sides) a dish in simmering water and then cover it completely (to prevent water from getting in) until it's cooked?

This sounds a lot like sous vide which is currently becoming commonplace after having been niched to large-scale kitchens and avant-garde restaurants. There are lots of resources online (just Google it), Douglas Baldwin has a bit of the science behind it.

Would this work for cakes and breads?

Depends on what you mean by "work", but yes, you can cook dough or batter enough to turn it into something that isn't just dough or batter; proteins coagulate at simmering temperatures. Here's a recipe for bread rolls using this technique, for example. The one thing you won't be getting is a nice, hard, brown crust since the Maillard reactions behind it requires temperatures above water's boiling point (100°C).

Fully submerged is going to be a problem, as you'd need an airlock to allow air to escape so you don't end up creating a pressure cooker. (which would prevent the bread from rising). If you were going to try this, I'd look into fermentation airlocks and grommets to install on a mason jar lid, and then use the largest straight-sided mason jar that I could find. You could then submerge the jar fully, but leave the top of the airlock out of the water.

You'll want to place a rack or something at the bottom of the outer pot to ensure that there's water under the jar, so it's not getting heated directly from the stove. You may also need to weight the jar down, so it doesn't float on you, as the bread will be less dense than the water.

If you're not up to investing in quite so much supplies, and don't insist on fully submerged, there is a style of bread that's cooked on the stovetop, in a water bath -- Boston Brown Bread. Mind you, that's a quick bread made with part cornmeal and often rye flour, so it doesn't rise quite as much as a yeast bread. It also doesn't need oven spring like most yeast breads do.

There are also plenty of "cake" like British puddings that are steamed stove-top ... Figgy Pudding and Spotted Dick come to mind, but I'm sure any of the Brits on here could give us a longer list of names for you to look up. You could also search BBC's Good Food for "steamed pudding"