There have been claims of government watch lists, some substantiated and some not, for decades. There is a specific database that does exist, the Terrorist Screening Database, which feeds almost a dozen lists including the No Fly List, the Secondary Security Selection List, the Violent Gang and Terrorist Organization File, and so on. This database results from Homeland Security Presidential Directive / HSPD–6, which itself doesn't say what it takes to get on the list. There is no master list of lists for all governments, but probably the TSDB is the "list" of most concern. This list is maintained by Terrorist Screening Center of the FBI: this is what they say about themselves.
Definitive information on how to get put on the list is not available (the 2007 Inspector General audit of TSC processing of data suggests there are particular criteria, but they are redacted in the public release of the document), but one can learn at least from the case Elhady v. Kable that by the FBI's representation of its practices, "An individual may be 'nominated' to the TSDB by a federal government agency or foreign government", and
Nominated individuals are added to the TSDB if their nomination is
based "upon articulable intelligence or information which, based on
the totality of the circumstances and, taken together with rational
inferences from those facts, creates a reasonable suspicion that the
individual is engaged, has been engaged, or intends to engage, in
conduct constituting, in preparation for, in aid or in furtherance of,
or related to, terrorism and/or terrorist activities.
This requires a "reasonable suspicion that the individual is a known or suspected terrorist".
The court finds that
TSC may consider, but may not solely base its decision on, an
individual's race, ethnicity, religious affiliation, or "beliefs and
activities protected by the First Amendment, such as freedom of
speech, free exercise of religion, freedom of the press, freedom of
peaceful assembly, and the freedom to petition the government for
redress of stress of grievances
as well as
an individual's travel history, associates, business associations,
international associations, financial transactions, and study of
Arabic as information supporting a nomination to the TSDB
placement into the TSDB does not require any evidence that the person
engaged in criminal activity, committed a crime, or will commit a
crime in the future
Based only on that information, it would not seem likely that simply asking if you are in the database would satisfy the conditions for being added to the database. However, as also noted by the court in Mohamed v. Holder, "the Court has little, if any, ability to articulate what information is viewed by the TSC as sufficiently 'derogatory' beyond the labels it has provided the Court" – the courts don't even know what the criteria are. So really, it is unlikely but there's no way to know for certain.