Coolidge died of a massive heart attack in January of 1933, two months before the end of Hoover’s term. If Coolidge had been President, he probably would have died even sooner.
Would Charles G. Dawes have continued Coolidge’s policies?
My belief is that President Coolidge, who was a high-strung individual in spite of his "cool" demeanor, was shaken by the direction of the country by then. He saw the stage for its downfall under "Wonder Boy" Hoover and then ultimately driven off the cliff by the victory of the FDR criminal gang in 1932. Unfortunately, President Coolidge never took his health seriously, snacking a lot and the death of his son contributed to his stress.
That said, the continuation of "Coolidge Prosperity" under his watch in 1928 would have given the Republic strength and I think would have fortified the man.
He probably would have, although he doesn't seem to have gotten along all that well with the president.
By the way, Dawes wrote the melody to Tommy Edwards' 1958 hit song It's All In the Game