Hey tykenfitz,
Yes, PS1 light gun games work on the PS2. I'm not 100% sure of what that Freeshot gun considers as "normal" mode, but my guns also have a normal mode, which works with Konami games, but not well. I have several guns from different makers, and none of them are accurate with Konami games unfortunately.
I'd say if that Freeshot gun is accurate, it'd be a good solution. I myself prefer to have rumble or recoil in my gun, but I feel that accuracy is the most important factor.
I do feel that if you're really into light gun games, you'd really be missing out on a lot of great shooting games in Mame that are not available on the PS2 like Police Trainer, Sharpshooter, Bang!, hunting games and more. I myself feel that a pc light gun is a great investment. You can always look into making your guncon compatible w/the pc, but I haven't tried it myself.
Best of luck!