> By the way, the answer to your questions is yes.
If it matters, I recently ordered 6 hardcovers from an author who's book that I downloaded from libgen was so impressively written, well sourced and thought provoking that I just had to put his best works (the book I "stole" by downloading, and 5 of his other works) in my physical library.
On the flipside, I recently wanted to read a book (different author) so badly but it wasn't available anywhere for less than $100 since it's out of print, so I downloaded it and don't feel bad at all. I haven't read that one yet, and if I love it I might spend the money for a physical copy, but it wouldn't matter since it's out of print and used and wouldn't make a difference to the author (also, he's dead).
So you copying one page from a book in a library would still lead to some form of compensation, although one could debate whether it is fair or not, whereas using a P2P search engine to locate an online copy of a PDF would not.
Also, IMHO, the discussion of such online libraries should separate the topic of fair compensation of authors (I believe Norway or Finnland have "author stipends" paid by the government that one can apply) and the topic of locating and researching whether a book is what one needs or to one's liking.