Yes, they were insured, but it's complicated. It's complicated enough that two of my academic press sources include incorrect information.

It is true that government regulations meant NASA could not pay for life insurance, and it was out of reach of astronaut salaries, and the signed envelopes as a replacement insurance are indeed real, but it's simultaneously true all the astronauts had insurance when they flew.

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In a 1959 deal between Life magazine and the seven Mercury astronauts (arranged by the lawyer Leo De Orsay), each astronaut was paid $24,000 a year; this gave Life exclusive access to the astronauts and their families.

Some of the media claimed the astronauts were "cashing in". Gene Cernan (who went on to be the commander of Apollo 17) said

The original astronauts wanted to protect their lives and those of their familes. I mean, the press early on was following our kids to school. The exclusivity of the Life arrangement inhibited people from peeking over our fences and that kind of thing.

The media controversy led to the contract nearly being not renewed in 1962, but the Mercury astronauts took their case to Vice President Johnson, and John Glenn spoke with President Kennedy personally. The contract was renewed (this time for $16,250 a year), although to lighten the controversy over exclusive access, in September 1962 NASA added a post-flight news conference to give all journalists a chance to speak with the astronauts.

World Book signed on as well (and paid the majority of the deal, with $10,000), and both publishers also covered a $100,000 insurance deal. This insurance did unfortunately have to be used; it was paid out to the families of the astronauts who died in the Apollo 1 fire.

This insurance policy lasted all the way through Apollo 10.

The space travel accident insurance for Apollo 11 was formed by William Harlan (Harlan Inc.), John Smith (Harlan Insurance Service), Earl Bell (of Travelers), Morrison Deach (of Travelers), Robert Greer (of Cullen Central Bank and Trust) and C. Wardell Leisk (Austral Oil). It covered not just the space travel itself but "disease endemic to the lunar surface", so that if they, for example, died while in quarantine after the flight, they were covered.

Apollo 12 and Apollo 13 were covered by Frank W. Sharp of National Bankers Life. This seems to not be for the publicity so much as a financial scam.

During the same period, Mr. Sharp was making arrangements for several astronauts to obtain stock in National Bankers Life. [...]

In a deposition, Captain Lovell said that Mr. Sharp had told him the stock was “to provide for my family.” The astronaut said that he executed notes for the stock, but that Mr. Sharp suggested that Captain Lovell keep the notes. After receiving the stock, Captain Lovell was elected to the board of directors of National Bankers Life.

After Apollo 12 had returned from the moon, Navy Captain Charles P. Conrad said, he received a telephone call from Captain Lovell asking if he and other members of the crew wanted to buy some stock in National Bankers Life.

Captain Conrad said that he and the others did not want to buy any of the stock because of the price, but that shortly afterward he and four other astronauts, the crews of Apollo 12 and 13, received stock certificates for 4,500 shares each of National Bankers Life stock from Ling & Company, along with a bill for $128,250 each.

Sharp was charged with (and pled guilty to) one false entry in the State Bank and one count of selling unregistered securities. Unfortunately, it looks like the deal ended up preventing further fraud charges, because his general modus operandi was to loan money to politicians, sell them shares, then artificially inflate the stock's value so said politicians could cash out at a profit; by "coincidence", Preston Smith, the governor at the time, introduced two bank-friendly bills (he claimed he had no knowledge Sharp was interested).

Apollo 14 through 17 were covered by the National Space Club Scientific and Educational Foundation through Travelers Insurance ($50,000 each astronaut). This was from coaxing via Congressman Olin Teague of Texas who was on the House of Science and Astronautics Committee; the chairman of the same committee was a trustee in the association.

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So they were all insured, so why the signed envelopes, the "Insurance Covers" now coveted by collectors? Well, you might notice a wide variance in where the insurance came from; there was a time for each mission where the astronauts thought they would not be insured.

The idea for the Insurance Covers came from a representative of the Houston Manned Spacecraft Center Space Club. Essentially, the astronauts would autograph some envelopes and then get them postmarked (for Apollo 11, some for the day of launch, some for the day of the moon landing). There are enough covers and enough variance in pens and inks that they were likely signed over multiple days or weeks.

Some of the covers were also flown by the astronauts -- meaning not really "insurance" in the case of loss of spacecraft.

The tradition continued until Apollo 15 which upped the ante to the point it turned into a scandal, where the astronauts (Scott, Worden, Irwin) were pre-paid by a stamp dealer to take 100 covers, and those covers started being sold in West Germany. (The astronauts received Air Force reprimands and were moved to other NASA projects.) Because of the scandal, there are fewer Apollo 16 and 17 covers, but some do exist.

Sources:

AGI Report, Volumes 1-6 (1968). American Geological Institute.

Astronautics and Aeronautics, 1967 - Chronology on Science, Technology, and Policy. NASA.

Burgess, C. and Doolan, K (2003). Fallen Astronauts: Heroes who Died Reaching for the Moon. U of Nebraska Press.

Cavallaro, U. (2018) The Race to the Moon Chronicled in Stamps, Postcards, and Postmarks. Springer.

Daily News (29 July, 1971). If Moon Bugs Bite They've Got Insurance.

Kinch, S. (2010). Handbook of Texas Online, "SHARPSTOWN STOCK-FRAUD SCANDAL," accessed June 04, 2020, http://www.tshaonline.org/handbook/online/articles/mqs01. Texas State Historical Association.

Reuters (25 July 25, 1969). Astronauts, Insured Against Germs.

Scott, D. and Jurek, R (2014). Marketing the Moon: The Selling of the Apollo Lunar Program. MIT Press.

Waldran, M (1 August 1971). The Frank Sharp Affairs: Vast Scandal Stuns Democrats in Texas. The New York Times.