No. But if he had reported his illegal income and paid tax on it, the principal prosecution mechanism against him would have been undermined.
Wouldn't that have also gone against his fifth amendment rights? It would seem that he was damned if he did and damned if he didn't.
Capone:
"Well, you see sir, I made five million dollars by selling illegal booze on the black market, but I just want to make sure that I pay my fair share of my taxes on it."
Judge:
"That's great Al. As long as we get our cut, your fine."
Yeah, like that's going to happen. See the problem there?