Yes, but you would never find a highly sought out book that is available without a waiting list.
With physical books, this is possible since there is so much inconvenience involved in taking them out.
Moreover, in many cases, people don't actually search for books. They just go to the library and take a book that they find by chance.
When you have a situation in which everyone searches for ebooks all the time, it becomes very unlikely that you will find a good ebook that is available without a waiting list.
Physical books are much more expensive to reproduce than an ebook. I don't think that libraries which stock ebooks will find much success in trying to control how many copies of their books are "out there" at any time.
I think that they'd either allow members to simply get a copy of the ebook, or, as mahmud mentioned below, they would only allow access from within the library, and they'd try and regulate the amount of information you accessed.
Ebooks today are not much cheaper than physical books. A library that allows many concurrent copies to be made of highly sought out books would probably need to pay a very high price to the publisher.
With physical books, this is possible since there is so much inconvenience involved in taking them out.
Moreover, in many cases, people don't actually search for books. They just go to the library and take a book that they find by chance.
When you have a situation in which everyone searches for ebooks all the time, it becomes very unlikely that you will find a good ebook that is available without a waiting list.