What are the chances the gains here might be on the order where we could stop dosing cattle with antibiotics?
Factory farms, or concentrated animal feeding operation as it are sometimes called, are crowded and stressful for the animal. Hygiene, temperature and ventilation are often bad. In combination this create a environment where sickness is rampant and currently antibiotics is the primary tool to keeps it functioning enough to be profitable. Seaweed is extremely unlikely to replace antibiotics in those kind of operations.
I'm not sure that is entirely accurate. Prophylactic treatment to avoid diseases is one reason for antibiotic usage, but more growth promotion is a much bigger factor.
The main reason that cattle are fed antibiotics is that a low dose of antibiotics makes them grow faster.
This use has been outlawed in the EU, but according to [1] antibiotic use for other reasons has increased since then, so it sounds like farmers only claim to use antibiotics against diseases, when they are actually only interested in the growth advantages.