I've never been to the Cafe Carlyle myself but a quick perusal of their website shows this...
September 10 to September 28
SUTTON FOSTER ~ Tuesday – Friday at 8:45 p.m., Saturday at 8:45 p.m. & 10:45 p.m.
Cover Charge: Tues. – Thurs. General Seating: $90 per person/ Bar Seating: $50 / Premium Seating: $140
Fri. General Seating: $100 per person/ Bar Seating: $60 / Premium Seating: $150
Sat. General Seating: $115 per person/ Bar Seating: $60 / Premium Seating: $165
Looks like you'll have to do a little more than make a reservation and hope you're there at the right time. If you were planning to dress formally anyway then your question is someone moot.
"Pardon my prior Mcfee slip. I know how to spell her name. I just don't know how to type it." -Talulah