The ACLU, Enemy of the State

Back in 2004 the ACLU filed a lawsuit on behalf of an unknown internet service provider against the FBI challenging the FBI's use of National Security Letters, NSLs.

National Security Letters allow the FBI to obtain information from third parties, such as telephone companies, financial institutions, Internet service providers, and consumer credit agencies. In these letters, the FBI can direct third parties to provide customer account information and transactional records, such as telephone toll billing records. However, the FBI can't access the content of email/telephone conversions, they can only see the email address sent to or the phone number that was called.

Judge Victor Marrero of the U.S. District Court for the Southern District of New York ruled that the NSL statute was unconstitutional under the First and Fourth Amendments. So after the suit Congress had amended the statute.

But now the ACLU is after the gag orders within the amended NSL statute. The gag orders prevent third parties, contacted by the FBI, from revealing that the FBI had requested information about a specific individual.....
From Reuters

The appeals courts on Wednesday questioned a lawyer representing the U.S. government on whether the FBI violated free speech rights in placing the gag orders.

The government argues they are in place for national security concerns, such as keeping terrorists from learning what they are investigating.

"You can't tell me that any terrorist is going to make anything out of the fact you issued NSLs to AT&T and Verizon," said Circuit Judge Sonia Sotomayor, using a hypothetical example.

If there are no gag orders then terrorists/would-be terrorists will certainly find out that the FBI is tracking them. The NSLs specifically request information about a certain individual that is connected to an ongoing investigation relating to terrorism. So yes, a terrorist will find out if there are no gag orders.