I'm in the IT field, and I can tell you from first hand experience that I've had computers go out due to bad power during fast fluctuating brown outs. It hasn't been many, probably only about 5 (out of over a couple thousand computers) over the past 20 years; however, bad power CAN damage your computer. Additionally, every one of them was a desktop.
Before I bought my inverter generator, I tried to use as few electronics as possible while on the old regular genny. I didn't use any computers, televisions or stereos while on backup, because I didn't want to risk it.
You may never have a problem, but I do believe there is a slight risk.