Lag WILL affect your scores. I've experienced latency (input lag specifically) myself, between an old LCD and newer ones, not to mention playing between game mode and movie mode where the difference was 20ms or 120ms, and the difference is VERY noticeable. I can truly say that it makes a BIG difference to your ability to do well in a game. I swear, my first LCD TV had more lag time in game mode than the TV I have now did in movie mode, it was that bad.
I'll be honest though, before I actually experienced lesser lag times, I didn't realise it was why I was sucking so bad at games. Once I got a TV with much better lag times, I suddenly realized the difference. I got better lap times in racers and was able to control the car much more efficiently. All of a sudden, I was hitting the flippers too soon in pinball. I was able to react to enemy bullets in shmups quicker. My examples may seem kind of old-school for younger gamers (you young whippersnappers, LOL), but you get the idea. Don't get me wrong, I still suck at games (I'm 51, so, you know.....decrasesed reaction times and whatnot), but I suck a LOT less than I did before I got a LCD TV with smaller lag times.
It's just one of those things you don't really notice until you experience better. Like the difference between jamming to tunes on a cheapo stereo and a quality one. Once you do, you can't go back. Streaming games just aren't going to work for me. There is no way they will ever get lag times down to a tolerable level while streaming games, no matter how fast your internet connection might be, or how close you are to the servers, compared to dedicated hardware being used in your home. God bless you if you can tolerate the latency. I certainly can't.