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No, it's not. Almost, but not quite.
As close as you can come to that is going from Mandalay Bay all the way to the Sahara without stepping onto the Strip sidewalk.
You can take the elevated tram from Mandalay Bay to Excalibur, or the tram from MBay to Luxor, then the people mover from Luxor to Excalibur. From Excalibur, you can cross the pedestrian overpass to New York-New York or the Tropicana, and from either cross to the MGM Grand. You'll have to go out of doors to do that, though, so there goes the air-conditioned-splendor theory.
Now, you can travel from the MGM Grand to the Sahara in air-condioning on the Las Vegas Strip Monorail, but the stations on either end are outside.
All in all, though, the amount of time spent crossing Tropicana Avenue and the Strip on the pedestrian overpasses and waiting outside for the monorail is pretty minimal for traveling the entire length of the Strip.