No it will not and that cable runs like trash on a PS3 or Wii and simply will not work for the PS2 as you need something to convert the signal as the PS2 doesn't support VGA out of the box, but that cable works when it wants to as I bought one and the trashiest thing ever. You need a VGA box and a monitor capable of sync on green and not many have this capability. It took a while before I got mine finally running on VGA but I got an Innovation PS1 VGA box and a device to convert VGA to HDMI. Only thing that sucks is it is powered by the memory card port and the PS2 will not power it so I have my modded PS1 on top of it to power the box on. A lot of work and not really worth it as it will not be in progressive scan until you install a chip like the modbo 4.0 and enable the force 480p option on the BIOS of the chip. But after I got done and it was working properly with the VGA to HDMI converter I got a scaler with it to output in 1080i or 720p in every game and looks amazing.
PS3 CECH-2501A [CFW] & CECH-3001 [OFW]/ PS2 SCPH-3901 & SCPH-7501/ PS1 SCPH-5501
Mod Cobra 4.46 v7.00 w/ E3 Flasher [CFW] & Cobra ODE 4.50 [OFW]/ Mod HDD-OSD [Phat] & Modbo 4.0 [Slim]/ Mod MM3
HDD 1tb [CFW] & 640gb [OFW]/ HDD 640gb & OPL v0.92 w/ 1.5tb SMB