If you are honest then it gives me a good idea of what forms will be interested in you and it gives me great leverage (social proof) to be able to say in all honesty that you passed a 1st or 2nd round with a credible cponsultancy. It also shows your focus.
And for example if your interviewing at 2nd round with Deloitte, its hardly news that they are hiring and to contact them with candidates specultaively a) you can lose ownership if you have no mandate b) it will just annoy them as they have a PSL c) Id probably not get a response.
Whats better for me a recruiter is to understand why the other company is your preferred choice so that I can provide you with roles or advice according to your drivers and motivators and help you evaluate my role too.
I'd gain insignificant advantage in my job by you telling me that 3 or 4 branded company names are hiring. I know this already as they have adverts up all over Top Consultant and the internet and its a "under cover" role is probably retained anyway and paid for so it would be pointless. They'll be on my propsect list anyway so if it was that simple I'd already be working with them.
It can take 6 months or a year to win an account so start legitimately sending in CV's and with the big players its all tied down on fixed term contracts that have a tendering process.
In summary - you dont have much to worry about.