In theory, the Senate could do just that (they'd have to change their own standing rules, of course, and I really doubt Mitch could get 51 votes for such a change). Nixon v. U.S. was pretty clear that the courts have absolutely no role to play in interpreting what it means to "try" an impeachment.
It must be admitted, however, that White and Souter made some compelling arguments in their concurrences that the majority was wrong on this point (Souter famously suggested that if the Senate sought to convict or acquit on account of a coin toss, that might be so outside the bounds of the body's Constitutional duty as to allow judicial review), so I guess we won't know for sure unless and until they try.