Absolutely. The abundance is astonishing. If you want good shopping you should visit either Beijing or Shanghai. In Beijing visit a place called Silk Street. It's a large indoor market where many foreigners go to haggle for cheap goods. Often the clothing isn't actually fake, but just rejects from the production line. Perhaps the logo on that Adidas track jacket was a bit skewed (which is actually the case for me). Always aim to bargain for about 20-40% of the asking price. If they refuse, say it's too expensive and walk away. 90% of the time they'll shout to call you back and be more permissive of aggressive haggling.
As for Shanghai, the big fake clothing market called Xiang Yang Market recently closed down. The land was bought out in favour of a large new shopping mall (you won't find fake stuff there!). But there are tons of little shops scattered around Shanghai that sell the fake clothing that once was sold at Xiang Yang. Also, there's a road called Qi Pu Road (pronounced Chee Pu, oh and "lu" is mandarin for "road") that has tons of small shops like Xiang Yang, but it's more obscure and harder to find. Ask the concierge at your hotel.
The quality of fake items is actually very good. Except for shoes. Shoes are often sub-par, and fall apart easily. You'll see the workmanship on all non-leather sports shoes like Adidas and Converse and Puma and Nike. Try to stay away from fake shoes.
The quality of clothing, however, is actually quite astonishing, and nearly as if not just as good as their real counterparts (I'm talking about build quality). Sometimes the logo will be a little off (after all, they churn these things out and you can't expect them to spend too much time on the little Lacoste alligator) but that's a small price to pay.
As for the "higher end" items you're talking about, when it comes to Polo and Lacoste, most of the time the Polo shirts I see are mostly solid coloured. But they're very thick and made with relatively high quality fabric that will last a while. They do sell Lacoste striped polos. But they also sell tons and tons and tons of dress shirts branded as Polo, DKNY, Hugo Boss, Giorgio Armani, among others. There is a much larger variety of dress shirts than polo shirts. Polo shirts are only a small part of the underground market in China.
As for Nike, stay away from the shoes. In fact they don't fake many Nike shoes here. The popular brands tend to be the more casual/retro Adidas, Puma and Converse. When it comes to sports brands there are jackets and backpacks galore that seem to be quite high quality. Except often the zippers on the backpacks deteriorate rather quickly.
So, to recap, bargain bargain bargain, stay away from shoes, go to Qi Pu Lu in Shanghai and Silk Street in Beijing, and have fun.
One last thingdon't be afraid of obscure brands. Visit the independent fashion boutiques that litter Shanghai. You can find all styles of clothing. I suggest you visit a C-Pix franchise for a good selection of high-quality Threadless-like graphic tees for cheap (RMB 68 each). Also don't be afraid to visit the large shopping malls like those in Xu Jia Hui, or Times Square, Next Age and Plaza 66 (your hotel concierge will know about all of these). You can always pay a bit more for quality clothing there. Although stay away from reknowned-brand retail stores like Vero Moda, Burberry, Mont Blanc, Armani, Gucci and the rest. You're not in China to shop like you're in Europe.
Enjoy!
What a nerd and a fool I was.... Luckily, I grew out of that quickly in high school--so much so that I was proudly wearing home-made pajama pants to school at one point. Who cares what brand your clothes are so long as they look good on you. Frankly, I'm a bit wary of anyone who name drops the brands of clothing they wear during casual conversation unless someone explicitly asked for the brand. Offering up the information voluntarily and on a regular basis just comes off as a bit snooty or self-obsessed and maybe even a little insecure IMO. It's probably not that way for all people, but I've known plenty who really have done that just to show off. 
