Yes. Religious organizations that qualify to operate under Section 508(c)(1)(A) are a special kind of 501(c)(3) nonprofit that enjoy tax-exempt status without obtaining official recognition from the IRS.
Congress has enacted special tax laws that apply to churches, religious organizations, and ministers in recognition of their unique status in American society and of their rights guaranteed by the First Amendment of the Constitution of the United States. Churches and religious organizations are generally exempt from income tax and receive other favorable treatment under the tax law; however, certain income of a church or religious organization may be subject to tax, such as income from an unrelated business.
“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.” – Constitution of United States of America 1789, Amendment 1