As a very general guideline, no seaweed alone won't be sufficient as it isn't a broad spectrum fertilizer. It is basically just K (potassium).

But that also depends on the brand you use and its components. Some products are strictly low K so yes those would require additional sources of other nutrients to be added, especially nitrogen. Others are blended to provide N and additional micronutrients plus the K, others offer both N and K but no minerals, etc.

EX:
Bioform 4-2-4 Fish and Seaweed Fertilizer Plus Sulfur
Maxicrop Soluble Seaweed Powder 1-0-4
Maxicrop Liquid Seaweed Plus Kelp 2-0-6
Maxicrop Liquid Seaweed Plus Iron 0-0-1 + 2% Fe
Neptune's Harvest Seaweed Fertilizer (0-0-1) Plus (adds major and minor nutrients and amino acids)

In other words all seaweed is not the same just as all tomatoes or coffee are not the same. Compare the nutrient breakdowns of each particular brand name and you may have to go to the manufacturers website to get the nutrient info.

The goal is to provide the plants with a basic level of a broad spectrum of nutrients N-P-K plus minerals and micro-nutrients and that will usually require a "mixed" blend of some sort. Look into some of the Earth Juice fertilizers and the fish plus kelp blends for a better balance of nutrients.

Hope this helps.

Dave

U da man Dave!