Yeah. Rocket first stage Approx. unfueled mass:

Super Heavy: 200000 to 280000 kg

Falcon 9 first stage (without Falcon Heavy side boosters): 25600 kg

So 200-280 tons. A standard barge can support 1500-3000 tons of cargo. Even with the added weight of a catch tower and a healthy factor of safety thrust isn't gonna sink the barge. Far more likely the major hurdle would be stability issues with how tall it is.

	▲	pixl97 an hour ago \| parent [-]
		It's not 280 tons... it's a falling object with kinetic energy so that rocket thrust is going to be very problematic for that boat especially if it' hitting unevenly. That and there's no way for it to stand without a catch tower.