Yes, the GE Silicone I rubber is commonly sold as bathtub caulking.
(That's a 'one' and not the letter 'I'.  The reason I used that symbol
is because GE refers to their rubbers as I and II).  This is also a
great glue for glass, a notoriously hard substance to glue.

I do not use Silicone I rubber for attaching cloth; here I prefer to
use PVC-E glue, commonly known as Player Piano Co. #320 glue.  PPCo
says it has a shelf life of six months, but I've had a large container
of it for close to 20 years, and it still works good as new.

Warning: PVC-E glue is totally different from PVC glue.  The latter is
used to glue PVC plastic pipe for plumbing uses and is a clear liquid
with a powerful, volatile smell like ether.  I am sure it is flammable.
On the other hand, PVC-E glue is white and smells exactly like "Elmer's"
glue, also known as white glue.  As a matter of fact, both these glues
can be confused with one another so the container should be clearly
marked.  PVC-E glue cures into a cloudy-clearish substance much like
rubber, while white glue cures into a cloudy-clearish substance that
will get rock hard.

As for Spencer Chase's comment about the difficulty in gluing wood that
has had silicone on it, let me say that I have heard for years that
silicone oil or grease or wax will soak into the wood, making painting
and gluing hard if not impossible.  However, GE Silicone I rubber comes
off wood completely, leaving no trace of coloration, or staining, or
odor or anything, leaving it no different from a new piece of wood.  At
least that is my experience.  The problem is that the word "silicone"
refers to countless things, up to and including  breast implants.

Randolph Herr