Potential issues with uploading copyrighted material to TurnItIn?
This is a bit long for a comment, but I also acknowledge that only someone from TurnItIn could categorically answer this.

Since TurnItIn does not provide access to source material (other than small sections which actually match the submitted paper), I do not see how it could be a copyright issue. I get matches all the time from papers submitted to other schools, yet, TurnItIn does not allow me to see that paper.

Additionally, much of the content within TurnItIn is under copyright (blogs and others) and they do not purge it, further implying that they would not have a problem with your plan.

All that said, unless the content is quite new, or changed regularly, as soon as one student includes content, any other student including that same content will trigger a flag for you.

So, I do not believe your plan will have any problem but I am also not sure you need to worry about it unless you have a special set of texts you believe other students around the world will not have access to.