You never know! You are off to a great start. One of my favorite rescue stories is Lane, of Doggie Debutantes. She was a breeder dog whose feet never touched the ground/grass for I think 2 years, was also kept in a horrible, squalid hutch. Now she lives an amazing life of activity and adventure, and a luxury wardrobe, lol. She has learned to play fetch, give kisses, cuddle with her parents and dog sister, play at doggie birthday parties, and more.
Check out the Doggie Debutantes Facebook page (Lane is the blondie):
https://www.facebook.com/DoggieDebutantes
Regarding Annie's eye problems, I agree with MissPixi about being careful what kind of grooming products you use. My Max had eye problems for awhile, corneal ulcers, and I only use SPA facial cleanser in the bath on his face. I don't use any saline -- and definitely no over the counter eye drops with him. He is allergic and will scratch his eyes.
I use lukewarm tap water on a cotton ball if I need to rinse anything out of his eye. Tap water is what goes in his eyes in the bath and he has been great with this for 2 years.
I would be inclined to take Annie to an ophthalmologist because that much watering is not normal. Most regular vets are not advanced enough to detect certain eye problems. Could be something that just requires special drops -- again, do not try over the counter drops -- they often make small problems worse.