No.
Impeachment is equivalent to an indictment. The House merely sits as a grand jury & votes on whether to indict based on the evidence it collects & the case that's built. This requires a mere majority. But during the process, the President ought to remain in office (as they do) with the full powers accorded to them by the Constitution, in part because the American legal system assumes innocence until proven guilty; in other words, innocence until conviction. Unless & until the Senate has held a full-blown trial that concludes with a 2/3rds guilty verdict, there ought to be no official reduction in or limitation on the President's authority.
I think the answer depends on the circumstances and the reasons the president is being impeached. If, for instance, the president were continuing to abuse his powers to obstruct an investigation during the impeachment process, it would be appropriate to invoke the 25th until the conclusion of the trial in the Senate in order to prevent the whole process from being tainted. Yes, in our criminal justice system the accused is innocent unless proven guilty, but the accused can still have their bond revoked and be remanded into custody if they continue to commit new offenses while awaiting trial.
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