2020, the election campaigns have begun

[hazard]

On at least 2 scenarios, January 20th arrives with no clear winner in the White House,

There's a line of succession: President (would be vacant), Vice-President (would be vacant), Speaker of the House (would still be Pelosi if they haven't met and selected a new Speaker).

So... the Dems would have control, if only temporarily.

Not necessarily.

If the election for the president is uncertain the election for members of the Congress of the United States may also still be uncertain. Including the seat for the current Speaker of the House. Because the Congress is constituted before the President is sworn in, but no elected representatives of the people of the United States also means no House of Representatives.

The next US president might be the president pro tempore of the Senate instead, which would have to be one of the 66/67 still seated senators and traditionally is assigned by vote to either the oldest or the longest serving senator, I'm not sure which. Or any other senator, in accordance with the line of succession.