Yes, if you have a PS4 on firmware 9.00 or below. A long while back those in the hacking/jailbreaking scene realized that Sony uses individual PS2 emulators for their "PS2 Classics" releases on PS3 & PS4, each bundled with the game to run on game start. To save time, Sony seems to have just used a variation on the PCSX2 core so once this was discovered some very smart people extracted those emulators and made programs to turn ANY PS2 game into a "PS2 Classic" to run on PS4 (as long as it is jailbroken).
Specifically, a PS4 on firmwares 5.05, 6.72 and 9.00 are very easy and stable so you don't have to do a ton to jailbreak it. 30 seconds after boot and you're good to play.
I've been playing NCAA11 from PS2 this way but there was always one small issue where some textures were a little blocky (stadium shadows, clouds, some of the field). I'm in the process of fixing that. When I do it's a perfect 1080p upscaling of the game like you'd get on a PC but native on PS4.
In the case of those here, you just need to download from my link, jailbreak your PS4 and install the download. It's very simple.