Yes and No. It will work IF you purchase separate sync ports for your speedlights. I know the 430 does not have a pc port and am pretty sure the 580 does not either. all you need to do is go to flashzebra or call them up and they can set you up with them. they are around $15 but will allow you to use the pocket wizards.
Another important question is do you want to adjust your flash power by your camera or do you want to do it manually? Pocket wizard offers a ttl trigger for speedlights. The PWIII trigger you are asking about is a "dumb" trigger as it will only trigger your flashes and you will not be able to adjust the power or use your ttl functions with it. If you just want a trigger to fire your flashes I would recommend you save some money and get the new pocket wizard Plus X triggers. they are $99 vs $140. If you want to control the power of your flashes and or use the ttl functions I would recommend the Pocket Wizard Mini TT1 and Flex TT5 systems. you can read about each of these on the pocket wizard website.
Each flash must have it's own (separate Pocket Wizard) receiver, or, at the very least a dedicated slave for the second flash, either built in or as an accessory. I am not familiar with the Canon speed lights although I would expect any of recent manufacture would incorporate an integral slave function. Both should work on TTL settings.
My only experience with PWs was for remote shuttering of a single camera for long exposures with the camera (Nikon D-300) on Bulb setting. I found the PW system did not work as advertised for Bulb settings and long exposures. The problems I had may have been caused by radio interference in one case; however, a separate test in a radio free environment produced the same results.