Nah, the Senate can change the rules too. They can say that they won’t hold any impeachment trials if it takes more than 10 days for the House to present the articles after a vote.
And like I said above, they could also dictate who must present the case during the trial. Pelosi wants to play games, McConnell can play too. Force her to present the case herself. See if the House keeps her in the Speaker’s chair.
Read the Constitution. It says that the Senate has to immediately take up the debate.
https://www.govinfo.gov/content/pkg/CDOC-99sdoc33/html/CDOC-99sdoc33.htm
IV. Sequence of events at the beginning of a trial...................9
1. First a message(s) from the House of Representatives
is received containing the information that the House
has voted impeachment, adopted articles, and appointed
managers. The Senate then adopts an order informing the
House when it is ready to receive the managers to
present the articles of impeachment.................... 9