Hah! Frank got there first, just as I was posting. My comments still retained in full, though.
In a word ... No.
Some Strathearn weights have an "S" cane or "S with date cane" (e.g. S79 with the S above the numerals) or two separate canes for the "S" and the 2-digit date. Designs with a signature cane also appear without signature. Some, but not that many, also have a Script signed edition number and in a few cases "Strathearn" in script may appear.
Other weights, such as "Ice Pool" (a lump of granite encased in the clear dome) have an impressed "prunt mark" on the base, which is a "leaping salmon" but sometimes easily confused with a letter "S". Again, designs witn the "prunt mark" also appear without it.