No, that is no longer true.
First, in the few months of the pandemic, autopsies were halted within the US but resumed as early as May.
Second, co-morbidites do not erase the underlining cause of deaths.
For example, three major co-morbidity was hypertension, obesity, and diabetes but these are also common for heart disease as well. Yet heart disease remains the number one cause of death in the US.
That is because hypertension, obesity, and diabetes alone are not always a death sentence but they certainly do not help with the longevity.
Another common co-morbidity is influenza and pneumonia. Influenza leads to one pneumonia in severe cases but pneumonia rarely leads to influenza. Meaning if someone dies from pneumonia caused by influenza; then they died from influenza.
Diabetes, hypertension, and obesity do not cause covid and vice versa but, one or more of these elements can increase the chance of fatality of covid.
Obviously, the cure for these co-morbidities cannot be solved with a shot or two..
But covid can.