No. The Gustav Rapiers are 1630ish. The thinner rapiers with heavy ring guards are acceptable, but the Elizabethan rapier was definitely a heavier, wider blade. Think of a broadsword blade with a rapier type hilt. That said, that would be an officers or gentleman's blade. The sailors would have used a shorter, heavier hanger- sort of a proto cutlass, but without the figure 8 guard or basket hilt. Soldiers would have used a broadsword type blade with guards similar to the ones Daniel posted. Long blades are right out. Elizabeth decreed in 1576 that blades should be no longer than 36 inches. If you read the period sword manuals, the English blades are shorter and heavier. The longer, thinner Italian and French blades are derided as 'bird spits', and looked on as beneath the honour of an Englishman. The English fighting style is a very in your face, brawling style, and the continetal blades won't stand up.
Now for the $10 question - Are there any examples of this style " The sailors would have used a shorter, heavier hanger- sort of a proto cutlass, but without the figure 8 guard or basket hilt. " that are for sale?