Not if we read the text:
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.
Extracting the relevant bit:
Congress shall make no law... abridging the freedom of speech
Illegal immigrants and visitors "have" free speech because no laws may be enacted against it, period.