The PS2 should be able to read copied discs without a mod chip - only it won't boot games, but movies should be fine.
Older PS2's can be very picky on what media they will read. If you search about you will find some people can not get copied movies to play at all!!
I would really recommened get the cheapest DVD player you can find and play your movies through that - I have killed 2 PS2's now by play too many backed up movies on them!