If your notebook comes with a built in TV-Tuner, There shouldn't be any delay.. A Usb tv-tuner might have some delay but at the risk to quality loss, you could probably lower the resolution and fix that issue. But USB tv-tuners usually suck for the most part.
However, yensed makes a valid point, USB tuners will have a delay. PCMCIA (or integrated) will be the best options. You may also have to disable time-shifting if the software supports it.
Say if I were to use this TV tuner from HP, do you think I'd be able to play games like Halo 3 and Bioshock without any problems?
I would definitely shop around if you want that exact tuner. Here is one on Ebay for MUCH cheaper... I personally don't have much any experiences using an Express card tv tuner, So I'm not an expert. But It looks like it should work well. Though I still wouldn't expect great quality. Out of curiosity, Why do you want to hook your 360 up to your notebook?
I would definitely shop around if you want that exact tuner. Here is one on Ebay for MUCH cheaper... I personally don't have much any experiences using an Express card tv tuner, So I'm not an expert. But It looks like it should work well. Though I still wouldn't expect great quality. Out of curiosity, Why do you want to hook your 360 up to your notebook?
At the moment, I dont have a great tv for video gaming. But from the looks of it, I'm just gonna go out and buy one. I wasn't planning on buying the card from HP, I just threw that link up to reference the product.
Plus, I really don't want to spend a ton of cash on a maybe.