It's definitely work-able! Sounds like you've got a reactive girl. Google links on reactivity/etc.
To answer the question, I think "well socialized" means different things to different people. I mean, reactivity is fairly normal in a lot of dogs, and it's just something you have to work through. Check out youtube channel kikopup - she's got some great videos!
Jackson is far from perfect - he's got this high pitched alert bark that can drive anyone crazy, whenever someone walks in our house. He's got some crazy quirks. But I do enjoy that I can take him ANYWHERE and know he will be fine and go with the flow. He doesn't bark in the car, he can walk past any dog and not care (or maybe just give a sniff), he can handle a kid coming up to pet him, he can walk through a store and not drag me into it/out of it, he behaves in a guests home and I can trust him, he can go on vacation with us, and I realize I'm VERY blessed. But I also spent a ton of time with him.
He's out and about with me *almost* every day and I'm extremely lucky that I was able to do that with him, from the time I brought him home. Not everyone has the ability to do it, and luckily, my schedule allowed it. So I think that's why he's the way he is... because I've brought him almost everywhere he could possibly go, and let him experience all sorts of different things and situations, but I've also got a great communication with him in regards to training so he just tends to naturally behave and know what I want him to do.
Here's a good one: