After a day of researching the question, I have found that the answer is YES! Nonsuch Palace did in fact exist - emphasis on the word *did*. Construction on the palace started on 22 April 1538 - At this time, the King's third wife, Jane Seymour (and mother of his only legitimate son) had died soon after childbirth. The palace reportedly took 9 years to build, and was the greatest of all of King Henry's building projects. Contrary to what some have heard and believe, the palace was indeed finished! The cost of the construction was about £24,000 - a fortune for that time. The location of the palace was in Surrey.
Although few paintings of the palace exist to this day, it is said that it was richly ornate and decorated to rival the French King Francis I's palace, Chambord.
The style of the palace was a mixture of Medieval and Renaissance architecture, with tall, eight-sided towers at each end.
Upon the death of King Henry VIII, the palace was put in the hands of his son and successor, Edward I, and then to Mary I - she, however, sold the palace to the Earl of Arundel. Later, the palace did return to the Tudor family, as it was sold back to Queen Elizabeth I during her reign.
After Elizabeth called it one of her homes, the palace passed in and out of many royal hands, but was eventually destroyed in 1682 (or 1683) and pieces of it were sold to pay for gambling debts of its owner.
There is apparently no evidence of the palace where it once stood, but pieces of it are held at the British Museum. There is also a Nonsuch Park, and a Nonsuch Mansion - but don't confuse that with the grand palace!
I'd like to give a big THANK YOU to my Facebook friend who suggested this topic to me, and wanted to learn more about it! I hope whoever is reading this has learned a little bit - I know I did! What a fascinating palace history.