Assuming that it doesn’t land on any of the flat roofs that top the different sections of the building, then yes.
The standard delay on a grenade is 4–5 seconds (any more than this and there is considerable risk of the thing being picked up and thrown back, in normal use). In five seconds, a dense object will fall 125 metres. As the Burj Khalifa is 830m tall, this is about 700 metres short of reaching the ground. To be sure of reaching the ground before exploding, you would need a delay of at least 13 seconds.
Edit: On the veracity of the above photo, it is indeed a genuine photo and not photoshopped, though Cruise is undoubtably wearing a safety harness. Care of Sarah Madden in the comments, here is the video of him being dropped off and photographed by helicopter:
Personally, I would be scared out of my skin doing that, but let’s face it, most of us know someone with more guts than sense, and Cruise appears to be one of those people.
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