Most folks wouldn't add another pump to feed it. The general methods are to tee off from your tanks suction side, this way some of the water goes directly to the skimmer, or tee it from the tanks return pump. It's along the lines of not adding so many devices to the tank as to make it over complicated or that extra pumps add extra heat. If it was me, I'd increase the size of my return pump (if needed) rather than add yet another pump to my sump. Think of the extra maintenance, extra cords (as if there were not enough already), heat, etc... Not to mention that I wouldn't add a Rio brand pump to anything due to the problems they seem to have.

As to why I wouldn't mod the inlet pump, mainly because I don't think I've ever heard of anyone modding both. I'd be concerned that you might not push much water into the skimmer if you modded it to much. If I was not making it into a recirc skimmer I'd consider doing it if it was the only pump. If it quit pumping water into the skimmer, at least I could still make it a recirc and use the pump for that. Might want to try the mods one at a time. If you build it into a recirc with a modded pump, you might find that it works so well you won't want to mod the inlet pump.