I doubt that.

"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."

talks about Congress, not an executive branch. the latter can gag a person, or a company.

The First Amendment applies to all three branches of the government, not just Congress. The executive branch can attempt to obtain a gag order, but the 1st Amendment nonetheless places limits upon them.

See, for example, https://en.wikipedia.org/wiki/New_York_Times_Co._v._United_S...