Unfortunately, I think the property would make you immune to electric damage.
http://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9qd3
FAQ wrote:
Unarmed Strike: For the purpose of magic fang and other spells, is an unarmed strike your whole body, or is it a part of your body (such as a fist or kick)?
As written, the text isn't as clear as it could be. Because magic fang requires the caster to select a specific natural attack to affect, you could interpret that to mean you have to do the same thing for each body part you want to enhance with the spell (fist, elbow, kick, knee, headbutt, and so on).
However, there's no game mechanic specifying what body part a monk has to use to make an unarmed strike (other than if the monk is holding an object with his hands, he probably can't use that hand to make an unarmed strike), so a monk could just pick a body part to enhance with the spell and always use that body part, especially as the 12/4/2012 revised ruling for flurry of blows allows a monk to flurry with the same weapon (in this case, an unarmed strike) for all flurry attacks.
This means there is no game mechanical reason to require magic fang and similar spells to specify one body part for an enhanced unarmed strike. Therefore, a creature's unarmed strike is its entire body, and a magic fang (or similar spell) cast on a creature's unarmed strike affects all unarmed strikes the creature makes.
The text of magic fang will be updated slightly in the next Core Rulebook update to take this ruling into account.
—Pathfinder Design Team, 03/01/13
RAW says an unarmed strike counts the entire body as a potential striking surface (no matter how absurd it may be), so grounding would allow any part of it to be immune to electrical damage. While the potential is there for abuse, you have to remember that the character had to trade off a +1 enchantment on an item that has a hard cap of +5, and can't be quickly changed out unlike a backup weapon.
EDIT: Nevermind, found the abuse. Nothing says you have to be a monk or actively using unarmed strike to have the benefit, and since anyone can technically make an unarmed strike, there's nothing saying that the wizard wears one with grounding, thawing, neutralizing, etc. If this ever came up in a home game, I'd take away the immunities, but still allow the saving throws and other effects.