In my journey to master the nuances of user impersonation in Windows I first had an issue about getting impersonation to a remote database to occur at all (see this SO question)
I dug into the internals of the connection pooling, and it turns out that Windows credentials are not considered a part of the connection pooling key at all. Only SQL logins would be taken into account.
So if there is an available connection that was opened under user A and you are now impersonating user B, it will still use it and SQL will see you as user A. The reverse is also true.
The approach of changing the connection string slightly for the two different users is fine. You might do this if you have a "normal" user and then you need to impersonate for some "elevated" user. Of course, you don't want a different string for every user of your application - otherwise you might as well disable connection pooling completely.
When tweaking your connection string, you might consider appending the impersonated username to either the Application Name
or Workstation ID
fields. This would have the benefit of setting up a separate pool for each impersonated user.