EE's are not botched anything, nor are they
Ameraucanas, I underline that as it is the correct spelling of the actual breed.
EE's come in many shapes and forms, but most commonly they are blue or green egg layers that have traits similar to Ameraucanas.
They really can lay any color egg, and they are wonderful chickens to have. Generally they are good layers and usually lay blue or green egg. but not always.
If your goal is a flock of colored egg layers, you most likely have those. As for passing on traits...yes and no.
For one thing, those are not "tufts"...those are "muffs" or "beards" . "Tufts" are an Aruacana thing, not Ameraucana and are completely different - they grow out of the ears. Yes they should return as the chicks feather in.
Most likely, two muffed and bearded birds bread together will produce muffed & bearded offspring.
The blue egg gene will most generally pass, as will the pea shape comb. So if they lay Blue or green eggs, so will their offspring.
Note: green eggs are a Blue egg/brown egg mix.
Now will they "return" to being an Ameraucana through successive breeding.....only if you bred them to Ameraucanas, and then bred back to Ameraucanas...again and again until you have removed all the non-Ameraucana genes! So in other words...no.
Gluing wood to steel, does not make it wooden steel, it makes it wood glued to steel
If the desired end result you speak of is to have True Ameraucanas, then you need to buy Ameraucanas, not Easter eggers.
I am sorry if you thought you did, but you did not.
Hatcheries do this every day, with every breed. If you buy a Rhode Island Red from a hatchery...it looks nothing like a Rhode Island Red should look!
And finally: Yes, an EE cross with a Welsummer makes an Olive Egger.