Anonymous resumes

I am in a situation where I must discreetly shop around for my next position. If you have read my other thread, you know that my company is conducting a search to replace an engineer that just left, the position will be made to be very similar to my current position, but with more of a networking slant. I can't just put my resume on Career Builder or whereever, because I would undoubtedly appear in my company's search results.

What I have done is put out an anonymous resume and confidential profile on Dice and Indeed with no personal information and omitting the name of my current company, I'm confident this obscures me enough to not send up any red flags. A company can just contact me through one of those sites, and I can choose to respond or not. But will this result in fewer contacts?

b