Yes! I used the dual input diode you linked instead of two separate diodes. Worked great and much easier and cleaner install...didn't make sense to me to use two.
Before you spend any money, I suggest you spend time reading through this thread. There are several posts explaining how to do exactly what you're wanting to do. Yes, it can be done. I have mine wired that way. All you need is is a diode and wiring (in addition to the lights, of course)!
Staun is what I use...love them! Adjust them initially to the PSI you want and they are set. Then just screw them onto each valve stem and they do the work while you enjoy the scenery. No babysitting each tire one by one. Once the tires are deflated, take them off and roll on...
This is actually the "forward cross" rotation meant for front wheel drive vehicles. The "rearward cross" method is recommended for 4WD vehicles. See cb4017's post above.