No, that’s not the case. An ATB is a tug and your sea time is the tonnage of the tug. You can count the combined tonnage of tug and barge on a 2 for 1 basis for up to half of the required unlimited tonnage time.* Third mate unlimited requires 1,080 days on vessels over 100 GRT and half of that time needs to be on vessels over 1,600 GRT. So with 540 days of sea time on a vessel over 100 GRT and 540 days sea time towing a barge with combined tonnage over 1,600 GRT you still need 240 days of sea time on a vessel that’s actually over 1,600 GRT for 3rd mate unlimited.
*I have heard of people getting their full unlimited license with just combined tug and barge time. That’s not supposed to happen but you might gamble $100 evaluation fee by applying and hoping the evaluator makes a mistake in your favor.