I haven't seen anything in my sources discussing a celebration, but I will look further shortly. My first belief is that celebration was unlikely, given the fact that the Holy Roman Empire and Austria itself were in a state of siege in 1800.

One thing to remember is that Napoleon had just taken power in France, and in 1800, had invaded Italy through Switzerland. Northern Italy, which was Austria's "back door". He had defeated the Austrians badly at Marengo in June, and his general Jean Moreau defeated another Austrian army at Hohenlinden in early December.

By December 8, the Austrian Army was in retreat from the outskirts of Munich to Vienna, and about 20,000 had been captured by the French by December 23. On December 25, with the French within 50 miles of Vienna, the Emperor's brother, Archduke Charles (who had relieved his other brother, Archduke John, of command) sued for peace, and the Treaty of Luneville was signed in January, dealing the Austrians a pretty humiliating final defeat - the HRE lost German territories on the left bank of the Rhine (IMPORTANT: Including Aachen, the burial place of Charlemagne and the site of dozens of Imperial Coronations), and Austria lost its claims to Tuscany.

Given that the anniversary of Charlemagne's coronation would have been on December 25, the timing was probably terrible.

This goes beyond the fact, though, that Charlemagne's coronation in 800 wasn't really the "birth" of the Holy Roman Empire. Modern historians see the coronation of Otto in 962 as being the founding date; I think your point though - that regardless of continuity, the coronation of Charlemagne would have been a potent symbolic moment - is likely correct. Had it not been for the War of the Second Coalition, there may have been substantial celebrations.

Sources: Rothenberg's Napoleon's Great Adversaries, The Archduke Charles and the Austrian Army, 1792–1814 & James Arnold's Marengo & Hohenlinden: Napoleon's Rise to Power; the Wikipedia pages on Hohenlinden and Marengo are both fairly well-written, and incorporate these sources as well.

EDIT TO ADD: Also, remember, Charlemagne's legacy was disputed and shared by the mostly-German HRE and the French. The 800 coronation in Rome was done by the Pope. In 1804, Napoleon would have the Pope come to Paris to coronate him as Emperor of the French. Napoleon called the crown he had made for the event the "Crown of Charlemagne". Source: Thierry Lentz, Napoleon and Charlemagne, found here: http://www.napoleon.org/en/reading_room/articles/files/lentz_charlemagne.asp

Follow up: to what degree did the Holy Roman Empire consider itself a direct descendant of the Roman Empire?

Wasn't the high medieval HRE a revival of the title? I'm not up on my history between the fall of the Western Roman Empire and the Battle of Hastings, but I'm pretty sure the HRE ceased to exist for a period there.

EDIT: To clarify, I'm actually asking, not trying to invalidate OP's question.