The reason for doing delayed fermentation in the fridge is that the yeast development is slowed down, while still allowing the enzymes that naturally occur in the flour to do their work (converting starches to sugars, making a more flavorful dough).
The risk of doing it on the counter instead of the fridge is that the enzymes are working AND the yeast is working, which can over-leaven the bread, and they'll eat up the sugars you are trying to create with enzymes. Over-leavened bread isn't ideal, but it isn't the end of the world either. There is a lot to learn about bread baking if you want to really excel at it, but "just bake it, it'll be fine" is always present as you experiment - glad the loaf turned out well!
"No-Knead" bread is a great introduction to "rustic" doughs (very high water content), and to cold fermentation. Cold fermentation is about the best thing you can do for your bread as a home baker, whether or not you are using the no-knead recipe - I cold ferment nearly everything I bake.
If you want to learn more about the process and jump off the deep end, Peter Reinhart's book "The Bread Baker's Apprentice" is a great place to start. It is detailed without being pedantic, simple without being over-simplified, and oriented for the home baker without forgetting the reasons that professionals do things the way they do.
I have to contradict @saj14saj here. I have frequently had bread made with underdeveloped gluten (my grandma uses AP flour and tends to knead very short, 2-3 minutes per hand, and use very short proofing times). The bread is soft and cakelike, but it has no trouble rising, and it is neither flat nor dense.
On the other hand, I have had bread with exactly the same symptoms as yours - first feeling great, then left out for a long time to proof. After that, it looks good, but one touch makes it collapse into itself. The reason was very clear: overproofing. There is no doubt that underdeveloped gluten cannot have been a factor in my case. First, I am experienced enough to know when my gluten is developed - the bread was kneaded well beyond windowpane test. Second, it was a large batch of dough. I baked the first loaf at the optimal time and it rose just fine and had a nice texture with traceable gluten sheets through the crumb. It was the second loaf, which I baked a few hours later (and the proofing loaf spent them in a 30 degrees celsius kitchen in summer) which made the trouble. The dough had exactly the "loose" feel you describe, unlike the normal, springy feel before the proofing. It collapsed on touch and would not rise at all. It also had a very strong yeast fermentation taste, unlike the other loaf.
From your description and my experience, my conclusion is that overproofing until your starter died in its own waste products is the most likely culprit. The simple answer would be to not let it sit out overnight. The right amount of time to let it sit would depend on the room temperature, on the amount of starter you used, but also its leavening strength, and that is a bit hard to judge for a newly created starter. My best suggestion is to use trial and error and maybe bake 4 hours after knocking instead of 8 next time, and the time after that adjusting with a smaller increment in the right direction depending on whether the bread turns out overproofed or underrisen.
Best Answer
Most yeast doughs develop additional flavor complexity if retarded in the refrigerator overnight, and there's nothing about a typical Stollen recipe that would cause anything to undermine retardation.
The only caveats: If you've already let the dough rise for several hours before retarding, there's a chance that you may not have enough food for the yeast to digest when the dough comes back to temperature, and the dough may not rise as much as you'd like. Also, if you've already shaped the dough with the almond paste inside, you'll need to take some care to seal in a bag without deforming the shape, and leave enough room in the refrigerator for the dough and the gases in the bag to expand.
But if you've only let the dough rise for an hour or so, as long as you refrigerate, the eggs won't be a problem, and you aren't likely to risk over-fermentation. In my experience, you usually need about 30-40 minutes time for the dough to become active again, assuming a moderately warm room.