Non Persistent Cookie In A Web Farm Using Classic Asp (3.0)

Im using classic ASP (3.0) and I have a web farm with 2 webservers
(webserver A and webserver B, both windows server 2003). I do not want
to store any client specific information on the webserver (therefore do
not intend to use the session object- as you cannot gaurantee which
server the user will go to). I want to store a small value (e.g. a Y/N
value or an Id) on the client machine for the duration of their
browsing session, hence I want to use a non persistent cookie (in
client memory) not a persistent cookie that will be written to disk as
a file.

Q. Therefore if I create a non persistent cookie (i.e. it resides in
the client browsers memory) and set this when the user was on webserver
A, can I read the value server side on subsequent requests even if the
user is redirected back to webserver B? As the webservers are part of
the same domain name Im assuming I can..?

Q. Using non persistent cookies (in client in memory) im assuming the
session Id that gets created by IIS has no use, as I am using client
side storage, hence it is worth disabling this on the webserver for
performance reasons?

Q. Is there a way, when using non persistent cookies that the client
user can see the values of this cookie client side, are their any
downloadable tools for example they can run?

Im aware of the issues with size of using cookies and users can disable
them, my question is more related to using them in a web farm. Im also
not intended in the short term to upgrade to asp.net as Im aware there
are alternatives for state storage in this. I hope someone can clarify
these points for me. Note: I see many articles talking about cookies
but none relating to web farms and cookies, those that do talk solely
about the session object (Server side), none really go further to talk
about (non persistent / persistent cookie usage with web farms client
side.