The answer is no for session. These are user based and it is not possible to share data using this mechanism.
However, there are a few other options you should consider.
1) If you are using the roles provider with ASP.NET (I take it that you are referring to ASP.NET) you should have a role assigned to each user. Using the roles provider you could easily distinguish between who is admin and who is a normal user.
2) Consider using application state. This is the same as session but is globally available to all users. There could be some token or information in the state that could be used to distinguish who is online etc. This is used in the same way as session state.
A Walkthrough to Application State
3) use the asp.net caching to store data or information:
Caching in ASP.NET