My roofer, who seems trustworthy, suggests that we pay him $1500 to treat our
slate roof with clear silicon to improve its longevity. I tried to
find references on the web as to how effective this practice is, and
have been unable. I want to find some intelligent analysis of how
effective this practice is.

Portions of the slate roof on the house I grew up in were installed in
the late 1800s and were in perfect condition. As slate roofs last
about a hundred years, I question whether a treatment is needed. More
likely you would have a problem with the underlying support structure
than the stone-- which is probably ten million year old-- wearing out
prematurely.

Silicon treatment sounds unnecessary for slate as the previous comment
points out. However, it is widely used to protect brick work etc from
water penetration. There are various silicon based products used for
this purpose. I think some of the products go under the tradename of
Aquacrete. Try the GE website under building and construction products
for more information.

re my previous comment. The website that you want is actually
www.protectosil.com  its actually degussa products not GE and its
aquatrete
Should find everything you need here by region.
Personally I dont think slate needs it.