Very incorrect. They would not have given the job to the president of the Senate to behave like a rubber stamp. They don't need to appoint anyone to the task if that is all it is.
The task is inherently discretionary. It has real power, and is not just ceremonial. The Constitution doesn't do ceremonial, it only deals with real exercises of power.
Had George Washington been the President of the Senate, and had he been presented with clearly corruptly produced results, he would not have said "Oh dear me! I *MUST* approve this pile of corruption, or people will talk bad about me!"
He would have said "No. Not on my watch."
The men of 1787 were not wilting flowers, they were honorable men who would not abide or participate in corruption. They would have rejected the corruptly produced results and sent the thing to the House for resolution.
George Washington would have been smart enough to know that holding a popular vote to select presidential electors was a dumb idea. In 2020, the only vote that would have mattered to him was the selection of presidential electors that took place on December 14th, not the silly "Election Day" nonsense of November 3rd.
Keep in mind that Washington was elected President at a time when most states did not have a popular vote to select their presidential electors.