No.
If you're asking if you buy a gun on Monday, and then go to another dealer and buy another gun on Tuesday, I wouldn't worry.

But if you buy 2 handguns on Monday, and then 3 handguns at another dealer on Tuesday, and then another 2 handguns at another dealer on Wednesday, it might raise some red flags. But even then, there's really nothing CBI can do if your NICS comes back clean. Buying a lot of guns sporadically doesn't put you on a "list". What puts you on a "list" is if the guns you purchase start ending up at crime scenes...