Mostly it takes T or T+1 days. A rare case of long time. ICICI is known for such things at many branches. The one I have at my place is best as staff don't believe in delaying things.
Anyways, yesterday morning around 11 AM, a friend opened at Unity Branch too. Got acc. no. and cust id from branch over call after 2 PM and it activated instantly. No Aadhaar used. But at same time PNB recently took 7 days to open offline account for one of my cousin. He was fed up but once it opened everything calmed down.
So depends on how branch handle things.