I applied for my Citi Platinum MC and Citi Amex within 2 weeks of one another and was approved instantly in the case of the MC, and after a week or so for the Amex.
When I applied for the CitiBusiness MC in early September I was instantly approved. I applied for the CitiBusiness Visa and Citi Gold MC within minutes of each other on Friday night and was approved for both immediately.
I plan on churning these once I have spent the requisite $250 and will share my findings then.