Early sea water had a very different osmolality than blood plasma.
The reference range of serum osmolality is 275–295 mosm/kg (mmol/kg) (MedScape). The osmolarity of sea water is about 1000 mOsm/l (Wikipedia), but it can vary substantially between different seas, namely between 642 and 1,480 mOsm/kg (Ninawe & Banik, 1998). ...
The argument that blood plasma resembles sea-water, in essence, relies on the notable similarity in concentration of two ions in plasma and sea-water, compared with their intracellular concentration: sodium and potassium.
The concentration of sodium-ion in sea-water is about 450 mM, whereas the concentration of potassium-ion is only about 10 mM (ref)
Even shorter answer: This can be easily (well, not that easily since you need to convert mols to milligrams) answered by looking at your last lab result.
Say you had Na: 135 mmol/ml on there which would be a plausible value. That's 135*22.88/1000 mg/ml or 3.1 g/l. Sea water has around 19 g/l, so that's a clear, definite "no".
It wouldn't be quite such a ...