Thanks, TJ.
I'll concede that the stormtroopers had been alerted to the danger, but I'd like to point out that the passage indicates that they were entering the holding office, where the duel with Yoda began, which was beneath the Rotunda -- suggesting they'd been tipped off by Mas Amedda (who witnessed the beginning of the duel in the office, but not its progression into the Rotunda).
"He flicked a finger, and in the Chancellor's Podium a dozen meters away, a switch tripped and sirens sounded throughout the enormous building; another surge of the Force sent his pod streaking in a downward spiral to the holding office at the base of the Podium tower. Clone troops were already swarming into it [the holding office at the base of the Podium tower]."
They were close, but not in the same room as either Yoda or Palpatine during the final stage of the duel. It probably would have been cutting it close, but the troops were breathing down Yoda's neck, either.