Yes, but that is just the 2nd part of the puzzle. The game (game developers) must first and foremost develop the game to support 1080i/p before your FULL HD TV can take advantage of it.
As what is really happening, say on a PC. Your game is 1024x768 but your screen is 1920x1200. It's going to look quite bad when its being resized to a larger resolution. It becomes somewhat blurry. Crosshairs, text and so on.
Granted TV's do a better job of upscaling the image than PC monitors, but it will not make it a true crisp image unless the game supports 1080i/p naturally. As most console games are below 720p and look quite bad on big TV's. Lots of jaggies are revealed and such, or rather they get shown up more and parts being stretched.
Here is another list I found that was confirmed on one of the forums at Beyond 3D. A huge thread discussing the true resolution of games that a huge percentage are falsely advertised on the back of the box.
Playstation 3Call of Duty 3 (screenshot) ~ 1088x624 (2x AA)
Call of Duty 4 = 1024x600 (2x AA)
Conan (demo) = 1024x576 (no AA)
Def Jam Icon (screenshot) = 1152x648 (no AA)
Full Auto 2 (demo) = 1920x1080 (4x AA)
Jericho (demo) = 996x560 (2x AA)
Marvel: Ultimate Alliance (screenshot) = 1920x1080 (no AA)
MX vs ATV Untamed (demo) = 1024x576 (no AA) Thats just above standard definition.
720×576NBA07 (demo) = 1920x1080 (no AA)
NBA08 (demo) = 1920x1080 (no AA)
NBA Street Home court (screenshot) = 1920x1080 (no AA)
Pirates des Caraibes (screenshot) = 768x1080 (no AA)
960x720 en mode 720p
Ridge Racer 7 (demo) = 1920x1080 (no AA)
The Darkness (demo) = 1024x576 (no AA)
Tony Hawk's Proving Ground (demo) = 1024x576 (no AA)
Transformers (screenshot) = 960x1080 (no AA)
Virtua Figther 5 (screenshot) = 1024x1024 (no AA)
1024x768 en mode 1080p
Virtua Tennis 3 (demo) = 1920x1080 (2x AA)
WWE 08 (screenshot) = ? 640x720 ? (2x AA)
les edges ont l'aparence du 1280x720 mais d'apres certain artefact il semble que ce soit le resultat de la fusion de 2 buffers MSAA 640x720
PSN GAMESBlast Factor = 1920x1080 (no AA)
Calling All Cars (screenshot) = 1920x1080 (4x AA)
Go Puzzle = 1920x1080
GTHD = 1440x1080 (no AA)
Selection des vehicules en 1920x1080
Locoroco Cocoreccho = 1920x1080 (2x AA)
Pixel Junk Racers = 1920x1080
Rub'a'dub = 1600x1080 (no AA)
Stardust HD = 1280x1080 (no AA)
Sudoku = 1920x1080
Tekken 5 Dark Ressurection (screenshot) = 1920x1080 (no AA)
Xbox 360Call of Duty 3 (screenshot) = 1040x624 (2x AA)
Call of Duty 4 (screenshot) = 1024x600 (2x AA)
Conan (demo) = 1024x576 (no AA)
Fifa 2006 (demo) = 1024x576 (2x AA)
Fifa 2007 (demo) = 1200x675 (no AA)
Halo 3 = 1152x640 (no AA)
NBA Street Home court (demo) = 1920x1080 (4x AA)
NCAA Football 08 (demo) = 1024x600 (2x AA)
Oblivion (screenshot) = 1024x600 (2x AA)
Perfect Dark Zero (demo) = 1152x640 (no AA)
Pro Evolution Soccer 6 (demo) = 1024x576 (2x AA)
Project Gotham Racing 3 (demo) = 1024x600 (2x AA)
Ridge Racer 6 (demo) = 1440x810 (no AA)
Tomb Raider Legend (demo) = 1024x600 (2x AA)
Tony Hawk's Project 8 (screenshot) = 1040x585 (2x AA)
Virtua Figther 5 (demo) = 1024x1024 (4x AA)
Virtua Tennis 3 (demo) = 1920x1080 (2x AA)