No, Varys is a ruthless Machiavellian bastard like Baelish except he's so-called nicer to characters inbook which makes him seem more genial and harmless to most. The fact that Baelish put a knife to Eddard's throat and that he blatently lied about the knife to the Starks in the first place makes people think he's the supreme devil, while unfortunately there are more devils in KL including Varys. I think people got a rude awakening when Varys killed Kevan Lannister outright.
Oops, I'd forgotten about that. Did Varys support LF's story, or did he just not contradict it? I remember Varys telling Tyrion that he wouldn't expose Shae to Cersei, but that if Cersei asked the right question he would answer it truthfully. Similarly, Varys could have killed Ned in the dungeon or could have let him escape, but he let Ned's situation play out. If Ned had privately questioned him about LF's dagger story, there is a chance Varys would have told the truth, especially given the flimsiness of the lie.
While Baelish constantly quips and mocks people and outright lies, Varys has a different approach. He likes to let people draw their own wrong conclusions and run with that instead of outright lying. He also likes to misdirect by indirectly implying certain information which isn't obvious to the characters nor the reader on a first read what he is trying to say between the lines. Lastly whenever chaos is likely to ensue Varys is strangely silent despite his constant barage of whispers beforehand.
Varys was present when LF lied through his teeth about the knife. Either he didn't know (unlikely) the truth or he was quite pleased with the prospect that the Starks and the Lannisters were about to rip out each other's throats.
It is also quite a coincidence that Varys chose to tell LF and not Pycelle that Catelyn arrived because no other council member were available. According to Halfhand this was due to LF's connection with the Tully's. But Varys does nothing casual or by coincidence. It is said by LF that he and Varys traded secrets at that point.
I personally believe Varys was delighted with the prospect of a splendid little war.