Helping a newbie with too much time on their hands

[TooCheap]

I currently have a U.S. PS2 that I would like to play copied games on. I plan on using either CDClone or CDRWIN to copy the original PS1 games. After the copies are made, will they play in the PS2 without any mod-chips or patches? At this point, I'd like to avoid installing mod-chips for fear of damaging my new system. Any help, suggestions, or comments is greatly appreciated!

Thanks.