Yes, but that's not punishment for communicating or publishing ideas. You can admit things that can be used against you in a prosecution for a different crime, but you cannot be legally punished for merely communicating or publishing ideas. To use such an example as evidence that you are not free from consequence legitimizes the common sentiment that freedom of speech is a soft right that can be violated if we feel like it very strongly.
Exactly my point. The government has been overlooking Google's antitrust issues, and Google doesn't get immunity from that scrutiny because some GOP congressmen don't like its First Amendment-protected actions. The antitrust scrutiny (and especially its timing) may seem like a "punishment for communicating or publishing ideas," but it's really not.
They key word there is merely. The government can still punish you for your other actions. For instance, if you use your free speech rights to brag that you're dumping a pollutant into a river, which is unregulated and therefore legal, and the scrutiny you invited with your speech leads the government learn that you're also drug dealer, they can still prosecute you.