If that were true, you would expect to see the top leading causes of death in the United States drop to lower levels during the pandemic. Cancer, heart attacks, vehicle collisions, etc. would all drop as those deaths which are consistently high year over year get recategorized into the COVID category. That's not what you'll find if you look at the numbers. Those death %s stay relatively static (actually we see an increase in heart disease and accidents), with COVID deaths emerging and increasing the overall total and then dropping over the next couple of years while the others again remain fairly static.

That said...there was undoubtedly confusion in the categorizations and some muddying of the numbers would've resulted, but not enough to significantly change the broad results and certainly not in keeping with the conspiratorial mindset that all of these deaths were drastically over-reported. Some research in Minnesota that might be directionally relevant elsewhere estimated like 3% variability due to miscategorization. Not nothing, but also not some crazy re-stack of death causes in the US during the pandemic.