Varys, imho, IS a targ. Possibly a ******* of Aerion Targaryen during his exile in Lys. But i take his shaven head as an "Egg-like" clue, regardless. hiding the platinum blonde of house Targaryen. It also explains, somewhat, why he was chosen to offer up his... bits... for that sorcerers ritual (we are not told one way or the other, but i suspect the magician was a Priest of Rh'llor using the Blood (and flesh) of Kings)..
A really interesting theory actually. I thought this myself (the first part, not the gelding part - thought that is quite interesting in and of itself).
What's interesting is that the story so far, if you really think about it, has been a battle between Varys and Littlefinger. Ultimately they are the only two poker players at the table. Cersei is a fool and hack of the lowest order. Tywin was utterly predictable, if not efficient. Ned Stark never had a chance to play the game, because it just wasn't him - like Ser Barristan, they just aren't made for politics. By all accounts, Jon Arryn seemed like an affable servant but an easy pawn.
Littlefinger first killed Jon Arryn, which kick-started the cascade of events leading to a new war. He then killed Joffrey, which he tells Sansa he did for no real reason but misdirection.
“Always keep your foes confused. If they are never certain who you are or what you want, they cannot know what you are like to do next. Sometimes the best way to baffle them is to make moves that have no purpose, or even seem to work against you. Remember that, Sansa, when you come to play the game.”
In reality, though, I believe both of those were counter-moves to Varys. If we accept the theory that Varys is working for a return to Targaryen rule, then it would make sense that he would want to sew dissention in the body politic - making the realm unstable under House Baratheon (but really House Lannister). It's easy to see why killing Jon Arryn and seeing Ned Stark installed as Hand wouldn't work for Varys. Jon Arryn was on the verge of revealing the three children as illegitimate. True this would shake things up, but the timing was all wrong.
The murder of Joffrey is the same story, but with a different twist. Tyrion gets framed, and I'm sure Littlefinger fully expected him to be executed or at least taken out of the game completely. This leaves Tywin to rule, without the Joffrey-Cersei stupidity that inflames the entire realm. Make no mistake about it, Varys is in favor of Cersei (through Joffrey or by herself) having full rein. He knows she is emotion-driven, impulsive, and highly prone to overestimating herself, always favoring overreaches that ultimately further destabilize the realm.
By killing Joffrey, Tywin is the effective reagent. It's true that Tywin could corral Joffrey on his own, but the problem there is the Tyrells. With Mace Tyrell and Margaery with their claws in the game, it makes things at least a little less predictable (we will see that this match was at least secondarily arranged by Littlefinger). Now GRRM takes great pains to make it seem like Tywin is all-powerful, all-knowing... someone who can solve any problem with wits and his vast personal wealth. That being said, he's a highly predictable, if not stabilizing force. Littlefinger knows Tywin has had more than enough of Cersei, and trusts that Tywin will send her back to Casterly Rock with Joffrey dead so Tommen can't be similarly poisoned by her. As I mentioned, getting rid of Tyrion would be a secondary gain - Tyrion seems to be the only one smart enough to play chess with Littlefinger, and with him gone it makes the tables a little more manageable.
Anyway, if this seems convoluted, its because it is. This is just what I believe, based not only upon my reading but also in hints from the TV show. It seems (especially in season 1 and 2) that the writers took pains to highlight the rivalry between Varys and Littlefinger.