What you want is possible.
This[
^] is a very good article on session handling. The part that is most relevant to you is
here[
^], you can store session in an SQL server. This is intended for web-farms/load balanced environments, but it should cover your scenario.
If you can't use the SQL Session Mode, your other option is to hand-roll your own custom provider, described
here[
^], in this case you can write to any backing-store you like.