I can think of absolutely NO reason at all to believe that. The Sith is an organisation; unless they wear badges I can't see anything special about being a Sith whick makes them identifiable.
We also have no indication that Lightning is Sith only. It's not as if Obi-Wan said "Blimey, he must be a Sith!" when Dooku did that. And Sidious simply had confidence in Maul's supreme swordfighting, is all. He didn't use ANY tricks at all except his skills! He could just have easily have been a super-skilled Jedi swordsman, like Mace.
It's not canon, of course, but the website agrees with me:
"Dooku escaped, with the Jedi aware of his succumbing to the dark side, but yet still unaware of his Sith allegiance."
I think you will find, for sure, that by episode III they are not treating DOoku as a Sith and will be surprised when they find out he is.