[The President] may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper.... Article II, Section 3
No!. Upon the senate being gaveled in in January PDJT needs to file an emergency writ of mandamus with the USSC demanding that the house immediately send the article of impeachment to the senate and if they refuse then the USSC should declare that the articles of impeachment is null and void. The senate needs to join the writ and also demand the articles be sent to them. The house needs to get a strong rebuke by the USSC.