The facts
70" Sony XBR2
PS2-Via Component into NAD receiver
NAD Receiver-Via HD Component into TV

The video I'm getting looks very grainy. Is this typical because of the size of my display?

It's typical because it's games from an eight-year old console being displayed on huge and tech-modern HDTVs. The graphic limitations are greatly magnified. My PS2 games on my SXRD XBR HDTV look exactly the same on my old PS2 as they do on my PS3.