NO!!!!! This is often one of the first things I ask when doing a tech consult for a new person: "are you using a two-prong or three-prong outlet?"
You should NEVER, EVER, EVVVVVERRRR run any computer ungrounded when that computer has a hot/return/neutral power supply! This certainly includes many, if not most, desktop computers using a three-pole teakettle plug. A static charge could build up in components in the case and burn out your system. (I once fried a '486 this way years ago, when I was still young and stupid, in a house that still had (and still does have) knob & tube wiring.)
Also, many PCs use the ground for timing, and if that's not available your data could be corrupted. If you touch the metal in your computer chassis, assuming there's exposed metal on its chassis (reach around back) and feel electrical shocks in your hand, you've got a ground problem or, in this case, no ground connection at all.
However, some laptops use (hopefully polarised) two-prong power cords--my two Toshibas are like this--so you needn't worry in that regard.
If you do try running your machine ungrounded and find it does somehow improve your reception, more power to you. But please, consider yourself warned!!