Yes - in a cookieless session the ID is added to the URL, in fact into the middle between the bit that defines the application and the bit defining the location within the application, as for example:
https://www.rspb.org.uk/applications/do ... mhvtcb3vf0
Clearly in a subsequent session the Id will be different and that recorded in a previous script will not be accepted. In fact when rerunning such a script ASP.NET continuously tries to redirect the browser to the new URL it has just invented (hence my interest in redirection).
The unfortunate effect is that one can record a script, and test it still works as long as one is within the session timeout period, but when running it later it fails (but without actually generating Server errors so it is possible not to notice).