Modern, properly working electrical devices do not trip a GFCI. But, it doesn't take much of an error for one to trip, but they are designed for PERSONAL safety, NOT equipment safety. A UPS, especially one that powers the load via the inverter constantly, will protect the most sensitive equipment, and all of them that I've seen, can output a signal that trigger the host computer connected to it to shut down gracefully, if required because the UPS is nearing the end of the battery charge. Don't know of any that will auto start the computer, but some computer bios can perform that function upon reapplication of power.