Just because you own something, doesn't give you the right to download a copy of it. You have to make the copy yourself, using the media you own. It is never legal to download copyrighted material. (Unless of course you are downloading it from the copyright holder, or an organization that has a distribution license).
Assuming everything went by the law and there was no piracy, this emu could also increase Sony profits. How? Sony makes a commission on each game sold. Originally the PS2(as well as PS3, unsure about PS4) was sold as a loss leader, which means it was sold at a loss with the loss expected to be made up by peripheral and game sales.
So, if everyone only played games they owned, and when games were available new, if a person bought a game to use with the emu, it would make Sony money.