Good question. Too many unknowns other then to say that currently B1 doesn't have that feature. (If it did, it would likely be under the alarm tile. That's where I saw it on the Band 2.)
In order to do Smart Alarm, some kind of processing has to figure out what stage you're in. I don't know where that's done now. Is it on the Band, in MS Health, or something done on the backend?
Band 1 cuts off all communication when in sleep mode. Since Band 2 isn't in the wild yet, we don't know what it does.
B1 could be limited by processor or by battery power. But without some input from those who know the details, I don't know as we'll have a answer.