Quick oats are cut thinly, steamed, and rolled flat (hence "rolled oats" as a name). The steaming partially pre-cooks them. The cutting and rolling makes them quick-cooking.
Other forms of oats are whole oats (uncut), and Irish or Scottish or "steel-cut" oats - none of which are steamed or cut thinly or rolled.
If you use any of these other kinds of oats, you will have a different result in your dish. It isn't about absorbency in particular - just that anything other than "instant" or "rolled" or "quick" oats will not likely be cooked in a recipe calling for a quick oat. (That is - they don't need more water - they need more time! And some quick-cook oats are used in recipies that don't call for ANY water - like cookies - because they are already cooked "enough" for the purposes of the recipe.)
However, you can use "regular" oats (not quick) in many recipes that call for quick oats. You will just need to cook them first. I would say NOT cookies, but bread. I wouldn't use them in apple crisp, either; you'd get a crisp with porridge on top. Maybe not a bad result, but not the result you'd be going for!
Signed, Alexandra the Oat Nerd