After you fill out the 3949-A and send lots of documentation does the IRS start to investigate?

The IRS may or may not investigate your claim. You'll never know from them unless they contact you for further information.

If he's already on their radar screen you are not eligible for a reward payment. Ditto if the information that you reported would reasonably have been discovered in the normal course of audit and collections actions.

Enclosing letters from the IRS related to the matter pretty much guarantees that he is on their radar screen and they are pursuing him for whatever tax he owes. Your 3949-A would most likely be ignored unless it exposed new information that they were completely unaware of and were unlikely to discover by any other means.

Yes, but it takes time. A month is a very short period of time. Your referral has to be researched, the file built, and the case sent to a group. The manager then assigns the case to a revenue agent. The revenue agent then has to research this person before contacting them. Six to nine months would not be an unreasonable time period before this person is contacted.