https://www.montecarlosbm.com/en/casino/game/prices-and-conditions-entry

The Monaco casino dress code is enforced at the entrance to Monte-Carlo Casino and visitors’ attire is subject to approval by Monte-Carlo Casino Management and staff. The dress code varies depending on the area and time of day.

Morning visits and visits to areas open to all (Atrium, Salle Renaissance, Café de la Rotonde, Le Salon Rose restaurant, Boutique):
You are asked to dress appropriately.
T-shirts, bermuda shorts and trainers/sneakers are permitted.

The games rooms (from 2pm):
You are required to dress appropriately.
Shorts (including bermuda shorts), jeans with rips or other cut-outs, sportswear, trainers, men’s flipflops and sandals, vest tops and beachwear are not permitted.
T-shirts and sweatshirts are not permitted after 7pm.

So if you want to go in to the gaming area, then no.